WHAT IS GEOSTATISTICS?
WHAT IS GEOSTATISTICS?
You need not be a statistician to make good use of geostatistics, but you may need the assistance, support, guidance of a (geo?)statistician. A good engineer, ecologist, biologist, plant scientist, hydrologist, soil physicist already has a good start, because geostatistics is only good science brought up to date by the recognition that natural phenomena are subject to spatial variation. Your study of geostatistics will not displace other knowledge that you have; rather, it will extend your knowledge and make it more useful.
(paraphrased from a quotation of William Edwards Deming)
A BIT OF HISTORY
The application of statistics to problems in geology and mining as well as to hydrology date back a considerable time. For a time, geostatistics meant statistics applied to geology or perhaps more generally to problems in the earth sciences. Beginning in the mid-60's and especially in the mid-70's it became much more closely affiliated with the work of Georges Matheron and perhaps that connection is still the prevailing one today. Because much of his early work and also that of his students appeared primarily in French it was not as well known in the US and other countries. Several events began to change that however. In 1975 a NATO ASI was held near Rome, Italy on Advanced Geostatistics in the Mining Industry. The proceedings contained papers that were primarily in English. This had been preceded by a set of notes (by Matheron) prepared for a summer program in Fontainebleau. These notes were in English but not readily available. A more definitive theoretical article appeared in the J. Applied Probability in 1973.
Professeur Matheron was at the Ecole Normale Superieure des Mines de Paris (School of Mines), one of the Grande Ecoles. As part of a general move of research units out from the main location in Paris (adjacent to the Jardin du Luxembourg), Matheron established the Centre de Morphologie Mathematique. Later this became two programs, one on mathematical morphology and on on geostatistics. Matheron retired as Director of the Center only last year. Jean Serra's two volume series on mathematical morphology and image analysis is well-known and is based on Matheron's earlier book on random set theory. Two of Matheron's students were instrumental in implanting geostatistics in North America. Andre Journel moved to Stanford University in 1978 and also co-authored Mining Geostatistics with Ch. Huijbrechts. Michel David had earlier moved to the Ecole Polytechnique in Montreal and in 1977 published Geostatistical Ore Reserve Estimation. Journel was in the Department of Applied Earth Sciences but more recently that department has been closed and he is now in the Department of Petroleum Engineering and has established (with the aid of various oil companies) the Stanford Center for Reservoir Forecasting.
Matheron's work was not very well accepted in the statistical community for a period of time although a number of prominent statisticians were visitors at Fountainebleau in the '70's, '80's and '90's. In part this was because of a feeling that some of the work was a duplication of results that were already well-known but with different names. Matheron's propensity to only publish in French and only in "internal notes" at the Center probably contributed to this perception. Now however, geostatistics has established a place for itself both within the statistics journals and at national meeings. In the mid-'80's, with the help of M. Armstrong, an index of those notes was published in Mathematical Geology, while it was possible to order zeroxed copies from the Center there was no generally accessible repository outside of the Center. The index noted above is now well out of date. Again with the assistance of M. Armstrong, a small number of these notes have appeared as journal articles. GLOSSARY
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Biostatistics-INTRODUCTION-
INTRODUCTION
(a portmanteau of biology and statistics; sometimes referred to as biometry or biometrics) is the application of statisticsto a wide range of topics in biology. The science of biostatistics encompasses the design of biological experiments, especially inmedicine, pharmacy, agriculture and fishery; the collection, summarization, and analysis of data from those experiments; and the interpretation of, and inference from, the results. A major branch of this is medical biostatistics, which is exclusively concerned with medicine and health.
Biostatistics and the history of biological thought
Biostatistical reasoning and modeling were of critical importance to the foundation theories of modern biology. In the early 1900s, after the rediscovery of Mendel's work, the gaps in understanding between genetics and evolutionary Darwinism led to vigorous debate among biometricians, such as Walter Weldon and Karl Pearson, and Mendelians, such as Charles Davenport, William Bateson andWilhelm Johannsen. By the 1930s, statisticians and models built on statistical reasoning had helped to resolve these differences and to produce the neo-Darwinian modern evolutionary synthesis.
The leading figures in the establishment of this synthesis all relied on statistics and developed its use in biology.
- Sir Ronald A. Fisher developed several basic statistical methods in support of his work The Genetical Theory of Natural Selection
- Sewall G. Wright used statistics in the development of modern population genetics
- J. B. S Haldane's book, The Causes of Evolution, reestablished natural selection as the premier mechanism of evolution by explaining it in terms of the mathematical consequences of Mendelian genetics.
These individuals and the work of other biostatisticians, mathematical biologists, and statistically inclined geneticists helped bring together evolutionary biology and genetics into a consistent, coherent whole that could begin to be quantitatively modeled.
In parallel to this overall development, the pioneering work of D'Arcy Thompson in On Growth and Form also helped to add quantitative discipline to biological study.
Despite the fundamental importance and frequent necessity of statistical reasoning, there may nonetheless have been a tendency among biologists to distrust or deprecate results which are not qualitatively apparent. One anecdote describes Thomas Hunt Morganbanning the Friden calculator from his department at Caltech, saying "Well, I am like a guy who is prospecting for gold along the banks of the Sacramento River in 1849. With a little intelligence, I can reach down and pick up big nuggets of gold. And as long as I can do that, I'm not going to let any people in my department waste scarce resources in placer mining.
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Quality control-INTRODUCTION-
Quality control, or QC for short, is a process by which entities review the quality of all factors involved in production. This approach places an emphasis on three aspects:
- Elements such as controls, job management, defined and well managed processes,performance and integrity criteria, and identification of records
- Competence, such as knowledge, skills, experience, and qualifications
- Soft elements, such as personnel, integrity, confidence, organizational culture,motivation, team spirit, and quality relationships.
Controls include product inspection, where every product is examined visually, and often using a stereo microscope for fine detail before the product is sold into the external market. Inspectors will be provided with lists and descriptions of unacceptable product defects such as cracks or surface blemishes for example.
The quality of the outputs is at risk if any of these three aspects is deficient in any way.
Quality control emphasizes testing of products to uncover defects and reporting to management who make the decision to allow or deny product release, whereas quality assurance attempts to improve and stabilize production (and associated processes) to avoid, or at least minimize, issues which led to the defect(s) in the first place.For contract work, particularly work awarded by government agencies, quality control issues are among the top reasons for not renewing a contract.
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Benefits of being a Muslim-part 1-
Paradise (part 1 of 2)
Description: A two-part lesson providing a glimpse of Paradise and what it holds for the believer with reference to the Quran and the sayings of Prophet Muhammad (peace be upon him). Part 1: Definition and types of happiness and the desire of Paradise as a significant factor in motivating a Muslim’s behavior and sense of happiness.
Objectives
· To learn the definition and types of happiness.
· To realize that the desire for Paradise is a significant factor in motivating a Muslim to do good deeds.
· To become familiar by means of a modest prelude, the nature of the gardens of Paradise.
What drives us? What makes us do the things we do? What makes us happy?
Many people will answer maximizing pleasure and minimizing pain is the ultimate key to human happiness.
If so, how come people can be happy while in pain and unhappy while experiencing pleasure? If pleasure is not the only motivating force that drives us, what does? What desires must we fulfill to live a happy life?
For most of those who see happiness in the carnal, rather than the spiritual, it is pretty basic: desire to avoid pain and anxiety, desire to spend time with relatives, desire to eat, desire for sexual gratification, desire for companionship, and desire for recognition to name a few.
Life for such can be toilsome, provoking the plain query; what is it really aiming for? In their quest for happiness, all too often people fall short of achieving any kind of inner peace. We think that by always reaching higher and accomplishing more - more money, a better body, the perfect mate - we will automatically be happy. That is an illusion. People get caught up in chasing the materialistic dream under the illusion money can buy happiness until they discover the limits of materialism. Impressing the neighbors and envy of possessions leaves us devoid of passion and depth in our lives, leading to the Modern Man’s Paradox: Spiritual hunger in an age of plenty.
What is the paradox? Simply put, it is this: As members of certain materialistic societies have grown richer, they have grown less content with their lives. No society in the history of the world has ever enjoyed the standard of living known today in these societies: Incomes are up, prices are stable, unemployment is down, life expectancy is rising; they enjoy more freedom and opportunity than ever before. Even their poor live well by world standards. Yet in America, for example, since 1960, the divorce rate has doubled, teen suicide has tripled, violent crime has quadrupled, the prison population has quintupled, and some estimates put the incidence of depression in the year 2000 at ten times what it was in the year 1900. Americans are less happy today than they were 40 years ago, despite the fact that they make 2.5 times as much money. Our bellies may be filled, but we are left spiritually hungry.
To find out what really drives human behavior, two kinds of happiness must be distinguished: feel-good happiness and value-based happiness. Feel-good happiness is sensation-based pleasure. When we joke around or eat our favorite food, we experience feel-good happiness. This type of happiness rarely lasts longer than a few hours at a time.
Value-based happiness is a sense that our lives have meaning and fulfill the larger purpose of our existence by connecting us to Allah. It represents a spiritual source of satisfaction, stemming from our deeper purpose and values. Living a God-conscious life rooted in the values of the Quran and Sunnah, a Muslim is driven - beyond sensual pleasures - by the desire to make it to Paradise and to be safe from Hell after death.
Islamic values that take a person towards Paradise and away from Hell are the most significant factors in motivating a Muslim’s behavior and in contributing to his or her sense of happiness. The desire to achieve Paradise in the afterlife puts the meaning back into life, superseding all other desires, to bring a sense of direction. An empty lifestyle focused on wealth, possessions, drugs, alcohol, and sex is replaced with the hope of making it to Paradise, a sense of connection with God’s creation, and a life of devotion to Allah instead of wealth and possessions. A person is focused on pleasing Allah even at the cost of our fellow human beings' disapproval. One must remember that the jewel of Paradise is veiled by hardships.
To be happy, wake up from materialistic dreams and realize that nothing save Allah alone is capable of satisfying man!
Ultimate satisfaction will be in reaching our ultimate goal – Paradise, not in this world, where we are like travelers and strangers. Paradise is not God’s residence, or a spiritual state where one becomes a part of God, as some mistakenly think. Paradise is a spiritual and sensual residence of pleasure in which all one’s senses will be gratified to the fullest. It is an abode of manifold enjoyments for the faithful, its dwellers will not feel the least pain or sadness. A place where every aspiration will be finally realized.
Islamic Gardens
Jannah (a beautiful garden) has historically inspired beauty, something which can be clearly seen in the beautiful gardens which were present throughout the Muslim world, such as those in Persia, Spain, and India, typically designed as a sort of escape or peaceful seclusion from the outside world. Waterworks and fountains were a common inclusion in Muslim gardens for their free flowing beauty and soothing sound. Artificial decorative elements were used in Muslim gardens as well, including the making of carpet-like parterres, and artificial trees and flowers made of precious metals and gemstones.
For generations of Muslims, these gardens represented a kind of sacred art, the aim of which was to draw the visitor closer to God. Today, the Muslim gardens on earth are like shadows of the true Paradise. These gardens serve as reminders to mankind of the heavenly abode to which the righteous will return.
Shade is provided by canopies and pavilions. Emphasis is placed on creating a space that indulges all the senses. Fragrance is a common feature of Muslim gardens, and herbs were potted up to fulfill this role. The decking provides a space for teaching and relaxing. Muslim gardens never contain statues, carved stone fountains with figures, or representational sculptures. Islam does not allow the use of such images. Some Muslim gardens are so famed for their beauty that people come from far and wide to enjoy their tranquility. Among them are the Alhambra Palace garden in Granada, Spain, the Jag Mandir Palace garden in India and the Major Elle residence garden in Marrakech, Morocco.
The lush gardens created by Muslims are man-made inspirations for an earthly Paradise. A secret haven secluded from the outside world; a place of tranquility, meditation, reflection, and prayer. A modest prelude for what it is to come for believers in the Hereafter.
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The history of Algeria -introduction-
The history of Algeria takes place in the fertile coastal plain of North Africa, which is often called the Maghreb (or Maghrib). North Africa served as a transit region for people moving towards Europe or the Middle East, thus, the region's inhabitants have been influenced by populations from other areas. Out of this mix developed the Berber people, whose language and culture, although pushed from coastal areas by conquering and colonizing Carthaginians, Romans, and Byzantines, dominated most of the land until the spread of Islam and the coming of the Arabs. The most significant forces in the country's history have been the spread of Islam, Arabization, Ottoman and French colonization, and the struggle for independence.
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INTRODUCTION TO OPERATION RESEARCH
INTRODUCTION
Although it is a distinct discipline in its own
right, Operations Research (O.R.) has also become an integral part of the
Industrial Engineering (I.E.) profession.
This is hardly a matter of surprise when one considers that they both
share many of the same objectives, techniques and application areas. O.R. as a formal subject is about fifty years
old and its origins may be traced to the latter half of World War II. Most of the O.R. techniques that are commonly
used today were developed over (approximately) the first twenty years following
its inception. During the next thirty or
so years the pace of development of fundamentally new O.R. methodologies has
slowed somewhat. However, there has been
a rapid expansion in (1) the breadth of problem areas to which O.R. has been
applied, and (2) in the magnitudes of the problems that can be addressed using
O.R. methodologies. Today, operations
research is a mature, well-developed field with a sophisticated array of
techniques that are used routinely to solve problems in a wide range of
application areas
This
chapter will provide an overview of O.R. from the perspective of an Industrial
Engineer. A brief review of its
historical origins is first provided.
This is followed by a detailed discussion of the basic philosophy behind
O.R. and the so-called “O.R. approach.”
The chapter concludes with several examples of successful applications
to typical problems that might be faced by an Industrial Engineer. Broadly speaking, an O.R. project comprises
three steps: (1) building a model, (2) solving it, and (3) implementing the
results. The emphasis of this chapter is
on the first and third steps. The second
step typically involves specific methodologies or techniques, which could be
quite sophisticated and require significant mathematical development. Several important methods are overviewed
elsewhere in this handbook. The reader
who has an interest in learning more about these topics is referred to one of
the many excellent texts on O.R. that are available today and that are listed
under "Further Reading" at the end of this chapter, e.g., Hillier and
Lieberman (1995), Taha (1997) or Winston (1994).
A
HISTORICAL PERSPECTIVE
While there is no clear date that marks the
birth of O.R., it is generally accepted that the field originated in England
during World War II. The impetus for its
origin was the development of radar defense systems for the Royal Air Force, and
the first recorded use of the term Operations Research is attributed to a
British Air Ministry official named A. P. Rowe who constituted teams to do
“operational researches” on the communication system and the control room at a
British radar station. The studies had
to do with improving the operational efficiency of systems (an objective which
is still one of the cornerstones of modern O.R.). This new approach of picking an “operational”
system and conducting “research” on how to make it run more efficiently soon
started to expand into other arenas of the war.
Perhaps the most famous of the groups involved in this effort was the
one led by a physicist named P. M. S. Blackett which included physiologists,
mathematicians, astrophysicists, and even a surveyor. This multifunctional team focus of an
operations research project group is one that has carried forward to this
day. Blackett’s biggest contribution was
in convincing the authorities of the need for a scientific approach to manage
complex operations, and indeed he is regarded in many circles as the original
operations research analyst.
O.R. made its way to the United States a few
years after it originated in England.
Its first presence in the U.S. was through the U.S. Navy’s Mine Warfare
Operations Research Group; this eventually expanded into the Antisubmarine
Warfare Operations Research Group that was led by Phillip Morse, which later
became known simply as the Operations Research Group. Like Blackett in Britain, Morse is widely
regarded as the “father” of O.R. in the United States, and many of the
distinguished scientists and mathematicians that he led went on after the end
of the war to become the pioneers of O.R. in the United States.
In the years immediately following the end of
World War II, O.R. grew rapidly as many scientists realized that the principles
that they had applied to solve problems for the military were equally
applicable to many problems in the civilian sector. These ranged from short-term problems such as
scheduling and inventory control to long-term problems such as strategic
planning and resource allocation. George
Dantzig, who in 1947 developed the simplex algorithm for Linear Programming
(LP), provided the single most important impetus for this growth. To this day, LP remains one of the most
widely used of all O.R. techniques and despite the relatively recent
development of interior point methods as an alternative approach, the simplex
algorithm (with numerous computational refinements) continues to be widely
used. The second major impetus for the
growth of O.R. was the rapid development of digital computers over the next
three decades. The simplex method was
implemented on a computer for the first time in 1950, and by 1960 such
implementations could solve problems with about 1000 constraints. Today, implementations on powerful
workstations can routinely solve problems with hundreds of thousands of
variables and constraints. Moreover, the
large volumes of data required for such problems can be stored and manipulated
very efficiently.
Once the simplex method had been invented and
used, the development of other methods followed at a rapid pace. The next
twenty years witnessed the development of most of the O.R. techniques that are
in use today including nonlinear, integer and dynamic programming, computer
simulation, PERT/CPM, queuing theory, inventory models, game theory, and
sequencing and scheduling algorithms.
The scientists who developed these methods came from many fields, most
notably mathematics, engineering and economics.
It is interesting that the theoretical bases for many of these
techniques had been known for years, e.g., the EOQ formula used with many
inventory models was developed in 1915 by Harris, and many of the queuing
formulae were developed by Erlang in 1917.
However, the period from 1950 to 1970 was when these were formally
unified into what is considered the standard toolkit for an operations research
analyst and successfully applied to problems of industrial significance. The following section describes the approach
taken by operations research in order to solve problems and explores how all of
these methodologies fit into the O.R. framework
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What is Econometrics
Introduction
1.1 What is Econometrics?
The term “econometrics” is believed to have
been crafted by Ragnar Frisch (1895-1973)
of
Norway, one of the three principle founders
of the Econometric Society, …rst editor of the journal Econometrica, and
co-winner of the
…rst
Nobel Memorial
Prize
in Economic
Sciences in 1969. It is therefore
…tting that we turn to Frisch’s own words in the introduction
to the …rst issue of Econometrica for an explanation of the discipline.
A word of explanation regarding
the term econometrics may be in order. Its
de…ni- tion is implied in the statement of the scope of the [Econometric]
Society, in Section
I of the Constitution, which reads:
“The
Econometric Society is an international society
for the advancement of economic theory in its relation to statistics and mathematics.... Its main object shall be to promote studies that aim at a uni…cation of the theoretical- quantitative and the empirical-quantitative approach to economic
problems....”
But there are several aspects of the quantitative approach to economics, and no single one
of these aspects, taken by itself, should be confounded with econometrics. Thus, econometrics is by no means
the
same as economic statistics.
Nor is it identical
with what
we call general economic
theory, although
a considerable portion of this theory
has a de…ninitely quantitative character. Nor should econometrics be taken as synonomous with the application of mathematics to economics. Experience
has
shown that each
of these three
view-points,
that of statistics, economic theory, and mathematics, is
a necessary, but not by itself a su¢cient, condition for a real understanding of the quantitative relations in modern economic life.
It is the uni…cation of all three that is powerful. And it is this uni…cation that constitutes econometrics.
Ragnar
Frisch,
Econometrica, (1933), 1, pp.
1-2.
This de…nition remains valid today, although
some terms have evolved
somewhat in their usage. Today,
we would say
that econometrics
is the uni…ed study
of economic models,
mathematical statistics, and economic
data.
Within the …eld of econometrics there are sub-divisions and specializations. Econometric theory concerns
the
development
of tools and methods,
and
the
study
of the properties
of econometric
methods. Applied econometrics is a term
describing
the
development
of quantitative
economic
models and the application of
econometric methods
to these models using economic
data.
1.2 The Probability Approach to Econometrics
The unifying
methodology of modern econometrics was articulated by Trygve Haavelmo (1911-
1999) of Norway,
winner
of the 1989
Nobel Memorial Prize in Economic
Sciences, in his seminal
1
paper “The probability approach in econometrics”, Econometrica (1944). Haavelmo argued that quantitative economic models must
necessarily
be probability
models (by
which today we would mean stochastic). Deterministic models are blatently inconsistent
with
observed economic quan- tities, and
it
is incoherent
to
apply
deterministic models to non-deterministic data. Economic
models should be explicitly designed to incorporate randomness; stochastic errors
should
not
be simply added to deterministic models to make them
random. Once
we acknowledge
that
an eco- nomic model is a probability model, it follows naturally
that an appropriate tool way to quantify,
estimate, and conduct inferences about the economy
is through the powerful theory of mathe- matical statistics. The
appropriate method for a quantitative economic analysis follows from the probabilistic construction of the economic model.
Haavelmo’s probability approach
was quickly embraced by the economics profession. Today no quantitative work in economics
shuns its fundamental vision.
While all economists embrace the probability
approach, there has been some evolution in its implementation.
The structural approach is the closest to Haavelmo’s original
idea. A probabilistic economic model is speci…ed, and the quantitative analysis performed under the assumption that
the economic model
is correctly speci…ed. Researchers often describe
this as “taking their model seriously.” The structural approach
typically leads to likelihood-based analysis,
including maximum likelihood and Bayesian estimation.
A criticism of the structural
approach is that it is misleading to treat an economic model as correctly
speci…ed. Rather, it is more accurate
to view a model as a useful abstraction or approximation. In
this case, how should we interpret
structural econometric analysis? The quasi- structural approach
to inference views a structural economic model as an approximation
rather than the truth. This theory has led to the concepts of the pseudo-true value (the
parameter value de…ned by the estimation
problem), the quasi-likelihood function, quasi-MLE,
and quasi-likelihood inference.
Closely related is the semiparametric approach. A probabilistic
economic model is partially
speci…ed but some features are left unspeci…ed.
This approach typically
leads to estimation methods such as least-squares and the Generalized Method of Moments.
The semiparametric approach dominates contemporary econometrics,
and is the main focus of this textbook.
Another branch of quantitative structural economics is the calibration approach. Similar to the quasi-structural approach, the
calibration approach interprets structural models as approx-
imations and hence inherently false. The di¤erence is that the calibrationist literature rejects mathematical statistics as inappropriate for approximate
models, and instead
selects parameters
by matching model and data moments
using non-statistical ad
hoc1 methods.
1.3 Econometric Terms and Notation
In a typical application, an econometrician has a set of repeated measurements
on a set of vari- ables. For example,
in a labor application
the variables could include
weekly earnings, educational attainment, age, and other descriptive characteristics. We call this information the data, dataset, or sample.
We use the term observations to
refer to the distinct repeated measurements on the variables. An individual observation often corresponds to a speci…c economic
unit, such as a person, household,
corporation, …rm, organization, country, state, city or other geographical region. An individual observation could also be a measurement at a point in time,
such as quarterly GDP
or a daily interest
rate.
Economists typically denote variables by the italicized roman characters y, x; and/or z: The convention in econometrics
is to use the
character y to denote
the variable
to be explained, while
1 Ad hoc means “for this purpose”
– a method designed for a speci…c problem – and
not based on a generalizable principle.
the characters x
and z are used to denote
the conditioning (explaining) variables.
Following mathematical convention, real numbers
(elements of the real line R) are written using lower case italics such as y, and vectors (elements
of Rk ) by lower case bold italics such as x; e.g.
0 x1 1
x = B x2 C
B C
xk
Upper case bold italics
such as X are used for matrices.
We typically denote the number of observations by the natural number
n; and subscript the variables by the index i to denote
the individual observation, e.g. yi; xi and zi. In some contexts we use indices other than i, such as in time-series
applications where the
index t is common, and in panel studies
we typically use the double index it to refer to individual i at a time period t.
The i’th observation
is the set (yi; xi; zi):
It is proper mathematical practice to use upper case
X for random
variables and
lower case x for realizations
or speci…c values.
This practice is not commonly followed in econometrics
because instead we use upper case
to denote matrices. Thus
the notation yi will in some places
refer to a random
variable, and in other places
a speci…c realization. Hopefully there
will be no confusion as the use should be evident from the context.
We typically use Greek letters
such as ; and 2 to denote unknown
parameters of an econo-
metric model,
and
will use boldface, e.g.
or , when
these
are
vector-valued.
Estimates are
typically denoted by putting a hat “^”, tilde “~” or bar
“-” over the corresponding
letter,
e.g.
^
and ~ are estimates of :
The
covariance
matrix
of an econometric
estimator will typically be written using the capital
boldface V ; often
with a subscript
to denote the estimator, e.g. V b
= var pn
b
as the
covariance matrix
for pn
b
: Hopefully without causing confusion, we will use the notation
V =
avar( b ) to denote the asymptotic covariance
matrix
of pn
b
(the variance of the
asymptotic distribution).
Estimates will be denoted by appending
hats
or tildes, e.g. estimate Vb is an of V .
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