Breakthroughs in Statistics: Methodology and Distribution

612 Pages·1992·12.316 MB·English

by  G. A. Barnard (auth.), Samuel Kotz, Norman L. Johnson (eds.)

Springer Series in Statistics
Perspectives in Statistics
Advisors
1. Berger, S. Fienberg, 1. Gani,
K. Krickeberg, I. Olkin, B. Singer
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Springer Series in Statistics
AndersenlBorganlGilllKeiding: Statistical Models Based on Counting Processes.
Andrews/Herzberg: Data: A Collection of Problems from Many Fields for the Student
and Research Worker.
Anscombe: Computing in Statistical Science through APL.
Berger: Statistical Decision Theory and Bayesian Analysis, 2nd edition.
BolfarinelZacks: Prediction lheo!'j fo! Finite "P()\)\l\at\()l\~.
Borg/Groenen: Modern Multidimensional Scaling: Theory and Applications
Brema.ud: Point Processes and Queues: Martingale Dynamics.
Brockwell/Davis: Time Series: Theory and Methods, 2nd edition.
DaleylVere-Jones: An Introduction to the Theory of Point Processes.
Dzhaparidze: Parameter Estimation and Hypothesis Testing in Spectral Analysis of
Stationary Time Series.
FahrmeirlTutz: Multivariate Statistical Modelling Based on Generalized Linear
Models.
Farrell: Multivariate Calculation.
Federer: Statistical Design and Analysis for Intercropping Experiments.
FienberglHoaglinlKruskallTanur (Eds.): A Statistical Model: Frederick Mosteller's
Contributions to Statistics, Science and Public Policy.
FisherlSen: The Collected Works of Wassily Hoeffding.
Good: Permutation Tests: A Practical Guide to Resampling Methods for Testing
Hypotheses.
GoodmanlKruskal: Measures of Association for Cross Classifications.
Gourieroux: ARCH Models and Financial Applications.
Grandell: Aspects of Risk Theory.
Haberman: Advanced Statistics, Volume I: Description of Populations.
Hall: The Bootstrap and Edgeworth Expansion.
Hardie: Smoothing Techniques: With Implementation in S.
Hartigan: Bayes Theory.
Heyer: Theory of Statistical Experiments.
HuetlBouvierlGruetllolivet: Statistical Tools for Nonlinear Regression: A Practical
Guide with S-PLUS Examples.
Jolliffe: Principal Component Analysis.
KolenlBrennan: Test Equating: Methods and Practices.
Kotz/Johnson (Eds.): Breakthroughs in Statistics Volume I.
Kotz/Johnson (Eds.): Breakthroughs in Statistics Volume II.
Kres: Statistical Tables for Multivariate Analysis.
Le Cam: Asymptotic Methods in Statistical Decision Theory.
Le Cam/Yang: Asymptotics in Statistics: Some Basic Concepts.
Longford: Models for Uncertainty in Educational Testing.
Manoukian: Modern Concepts and Theorems of Mathematical Statistics.
Miller, Jr.: Simultaneous Statistical Inference, 2nd edition.
MostelierlWaliace: Applied Bayesian and Classical Inference: The Case of The
Federalist Papers.
(continued after index)
Samuel Kotz Norman L. Johnson
Editors
Breakthroughs in Statistics
Volume II
Methodology and Distribution
Springer
Samuel Kotz Norman L Johnson
College of Business Department of Statistics
and Management Phillips HaJJ
University of Maryland The University of North Carolina
at College Park al Chapel Hill
College Park, MD 20742 Chapel Hill, NC 27599
USA USA
Library of Congress Cataloging-in-Publication Data
Breakthroughs in statistics I Samuel Kou, Norman L. Johnson, ediu)f'5.
p. cm. - (Springer series in statistics. Perspectives in
statistics)
Includes bibliographical references and index.
Contents: v. 2. Mclhodology - v. 1. Foundations and basic Iheory.
v. 2. Methodology and distribution.
ISBN-13: 978-0-387-94039-7
1. Mathematical statistics. I. Kou. Samuel. 11. Johnson,
Norman Lloyd. III. Series.
QA276.B68465 1993
jI9.j-dc20 93-3854
Printed on acid-free paper.
10 1992 Springer-Verlag New York, Inc.
All rights reserved. This work may not be translated or copied in whole or in part without the
written pennission of Ihe publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue. New
York. NY 10010. USA),excepl for brief excerpts in connection with reviews or scholarly analysis.
Use in conne<:lion with any (onn of infonnation storage and rctrleval, electronic adaptation,
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The use of general descriptive names. trade names, trademarks, etc., in this publication. even if
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Typeset by Asco Trade TyptSCtting Ltd., Hong Kong.
Printed and bound by Edwards Brothers, Inc., Ann Arbor, MI.
9876543
ISBN-I3: 978-0-387-94039-7 e·ISBN-13: 978-1-4612-4380-9
001: 10.10071978-1-4612-4380-9
SPIN 10j7Q243
To the memory of Guta S. Kotz
1901-1989
Preface
McCrimmon, having gotten Grierson's attention, continued: "A breakthrough,
you say? If it's in economics, at least it can't be dangerous. Nothing like gene
engineering, laser beams, sex hormones or international relations. That's where
we don't want any breakthroughs." (Galbraith, 1.K. (1990) A Tenured Profes
sor, Houghton Mifflin; Boston.)
To judge [astronomy] in this way [a narrow utilitarian point of view] demon
strates not only how poor we are, but also how small, narrow, and indolent our
minds are; it shows a disposition always to calculate the payolTbefore the work,
a cold heart and a lack of feeling for everything that is great and honors man.
One can unfortunately not deny that such a mode of thinking is not uncommon
in our age, and I am convinced that this is closely connected with the catastro
phes which have befallen many countries in recent times; do not mistake me, I
do not talk of the general lack of concern for science, but of the source from
which all this has come, of the tendency to everywhere look out for one's advan
tage and to relate everything to one's physical well-being, of the indilTerence
towards great ideas, ofthe aversion to any elTort which derives from pure enthu
siasm: I believe that such attitudes, if they prevail, can be decisive in catas
trophes of the kind we have experienced. [Gauss, K.F.: Astronomische An
trittsvorlesung (cited from Buhler, W.K. (1981) Gauss: A Biographical Study,
Springer: New York)].
This collection of papers (reproduced in whole or in part) is an indirect out
come of our activities, during the decade 1979-88, in the course of com
piling and editing the Encyclopedia of Statistical Sciences (nine volumes and
a Supplementary volume published by John Wiley and Sons, New York). It
is also, and more directly, motivated by a more recent project, a systematic
rereading and assessment of Presidential Addresses delivered to the Royal
Preface
V111
Statistical Society, the International Statistical Institute, and the American
Statistical Association during the last 50 years.
Our studies revealed a growing, and already embarrassingly noticeable,
diversification among the statistical sciences that borders on fragmentation.
Although our belief in the unified nature of statistics remains unshaken, we
must recognize certain dangers in this steadily increasing diversity accompa
nying the unprecedented penetration of statistical methodology into many
branches of the social, life, and natural sciences, and engineering and other
applied fields.
The initial character of statistics as the "science of state" and the attitudes
summed up in the Royal Statistical Society's original motto (now abandoned)
of aliis exterendum ("let others thresh")-reflecting the view that statisticians
are concerned solely with the collection of data-have changed dramatically
over the last 100 years and at an accelerated rate during the last 25 years.
To trace this remarkably vigorous development, it seemed logical (to us)
to search for "growth points" or "breakthrough" publications that have initi
ated fundamental changes in the development of statistical methodology. It
also seemed reasonable to hope that the consequences of such a search might
result in our obtaining a clearer picture of likely future developments. The
present collection of papers is an outcome of these thoughts.
In the selection of papers for inclusion, we have endeavored to identify
papers that have had lasting effects, rather than search to establish priorities.
However, there are introductions to each paper that do include references to
important precursors, and also to successor papers elaborating on or extend
ing the influence of the chosen papers.
We were fortunate to have available S.M. Stigler's brilliant analysis of
the history of statistics up to the beginning of the 20th century in his book,
The History of Statistics: The Measurement of Uncertainty (Belknap Press,
Cambridge, Mass., 1986), which, together with Claire L. Parkinson's Break
throughs: A Chronology of Great Achievements in Science and Mathematics
1200-1930 (G.K. Hall, Boston, Mass., 1985), allowed us to pinpoint eleven
major breakthroughs up to and including F. Galton's Natural Inheritance.
These are, in chronological order, the following:
C. Huyghens (1657). De Ratiociniis in Aleae Ludo (Calculations in Games of
Dice), in Exercitationum Mathematicarum (F. van Schooten, ed.). Elsevier,
Leiden, pp. 517-534.
(The concept of mathematical expectation is introduced, as well as many ex-
amples of combinatorial calculations.)
1. Graunt (1662). Natural and Political Observations Mentioned in a Following
Index and Made upon the Bills of Mortality. Martyn and Allestry, London.
(Introduced the idea that vital statistics are capable of. scientific a~alysis.)
E. Halley (1693). An estimate of the degrees of mortahty of m~nkmd, drawn
from the curious "Tables of the Births and Funerals at the CIty of Breslaw;
ix
Preface
with an attempt to ascertain the price of annuities upon lives," Phi/os. Trans.
Roy. Soc., Lon., 17, 596-610, 654-656.
[Systematized the ideas in Graunt (1662).]
J. Arbuthnot (1711). An argument for Divine Providence, taken from the
constant regularity observed in the births of both sexes, Phi/os. Trans. Roy.
Soc., Lon., 27,186-190.
(This is regarded as the first use of a test of significance, although not de-
scribed as such explicitly.)
J. Bernoulli (1713). Ars Conjectandi (The Art of Conjecture). Thurnisorium,
Basel.
(Development of combinatorial methods and concepts of statistical inference.)
A. De Moivre (1733,1738,1756). The Doctrine of Chances, 1st-3rd eds. Wood
fall, London.
(In these three books, the normal curve is obtained as a limit and as an
approximation to the binomial.)
T. Bayes (1763). Essay towards solving a problem in the doctrine of chances,
Phi/os. Trans. Roy. Soc., Lon., 53,370-418.
(This paper has been the source of much work on inverse probability. Its
influence has been very widespread and persistant, even among workers who
insist on severe restrictions on its applicability.)
P.S. Laplace (1812). Theorie Analytique des Probabilites. Courcier, Paris.
(The originating inspiration for much work in probability theory and its ap
plications during the 19th century. Elaboration of De Moivre's work on nor
mal distributions.)
K.F. Gauss (1823). Theoria Combination is Observationum Erroribus Minimis
Obnoxiae. Dieterich, Gottingen.
(The method of least squares and associated analysis have developed from
this book, which systematized the technique introduced by A.M. Legendre in
1805. Also, the use of "optimal principles" in choosing estimators.)
a
L.A.J. Quetelet (1846). Lettres S.A.R. Ie Duc Regnant de Saxe-Cobourg et
Gotha, sur la Theorie des Probabi/itl~s, appliquee aux Sciences Morales et Po
litiques. Hayez, Brussels. [English Translation, Layton: London 1849.]
(Observations on the stability of certain demographic indices provided empir
ical evidence for applications of probability theory.)
F. Galton (1889). Natural Inheritance. Macmillan, London.
[This book introduces the concepts of correlation and regression; also mix
tures of normal distributions and the bivariate normal distribution. Its impor
tance derives largely from the influence of Karl Pearson. In regard to correla
tion, an interesting precursor, by the same author, is 'Co-relations and their
measurement, chiefly from anthropometric data,' Proc. Roy. Soc., Lon., 45,
135-145 (1886).]
In our efforts to establish subsequent breakthroughs in our period of study
(1890-1989), we approached some 50 eminent (in our subjective evaluation)
x Preface
statisticians, in various parts of the world, asking them if they would supply
us with "at least five (a few extra beyond five is very acceptable) possibly
suitable references ... ". We also suggested that some "explanations of reasons
for choice" would be helpful.
The response was very gratifying. The requests were sent out in June-July
1989; during July-August, we received over 30 replies, with up to 10 refer
ences each, the modal group being 8. There was remarkable near-unanimity
recommending the selection of the earlier work ofK. Pearson, "Student," R.A.
Fisher, and J. Neyman and E.S. Pearson up to 1936. For the years following
1940, opinions became more diverse, although some contributions, such as A.
Wald (1945), were cited by quite large numbers of respondents. After 1960,
opinions became sharply divergent. The latest work cited by a substantial
number of experts was B. Efron (1979). A number of replies cautioned us
against crossing into the 1980s, since some time needs to elapse before it is
feasible to make a sound assessment of the long-term influence ofa paper. We
have accepted this viewpoint as valid.
Originally, we had planned to include only 12 papers (in whole or in part).
It soon became apparent, especially given the diversity of opinions regarding
the last 50 years, that the field of statistical sciences is now far too rich and
heterogeneous to be adequately represented by 12 papers over the last 90
years. In order to cover the field satisfactorily, it was decided that at least 30
refer~nces should be included. After some discussion, the publisher gener
ously offered to undertake two volumes, which has made it possible to include
39 references! Assignment to the two volumes is on the basis of broad classifi
cation into "Foundations and Basic Theory" (Vol. I) and "Methodology and
Distribution" (Vol. II). Inevitably, there were some papers that could reason
ably have appeared in either volume. When there was doubt, we resolved it
in such a way as to equalize the size of the two volumes, so far as possible.
There are 19 introductions in the first volume and 20 in the second. In addi
tion, we have included Gertrude Cox's 1956 Presidential Address "Frontiers
of Statistics" to the American Statistical Association in Vol. 1, together with
comments from a number of eminent statisticians indicating some lines on
which statistical thinking and practice have developed in the succeeding years.
Even with the extension to two volumes, in order to keep the size of the
books within reasonable limits, we found it necessary to reproduce only those
parts of the papers that were relevant to our central theme of recording "break
throughs'" points from which subsequent growth can be traced. The neces
sary cutting caused us much "soul-searching," as did also the selection of
papers for inclusion. We also restricted rather severely the lengths of the
introductions to individual items. We regret that practical requirements made
it necessary to enforce these restrictions. We also regret another consequence
of the need to reduce size-namely, our inability to follow much of the advice
of our distinguished correspondents, even though it was most cogen~l! advo
cated. In certain instances the choice was indeed difficult, and a declslOn was
Xl
Preface
reached only after long discussions. At this point, we must admit that we have
included two or three choices of our own that appeared only sparsely among
the experts' suggestions.
The division between the two volumes is necessarily somewhat arbitrary.
Some papers could equally appear in either. However, papers on fundamental
concepts such as probability and mathematical foundation of statistical infer
ence are clearly more Vol. I than Vol. II material (though not entirely so,
because concepts can influence application).
There have been laudable and commendable efforts to put the foundations
of statistical inference, and more especially probability theory on a sound
footing, according to the viewpoint of mathematical self-consistency. Insofar
as these may be regarded as attempts to reconcile abstract mathematical logic
with phenomena observed in the real world-via interpretation (subjective
or objective) of data-we feel that the aim may be too ambitious and even
doomed to failure. We are in general agreement with the following remarks
of the physicist H.R. Pagels:
"Centuries ago, when some people suspended their search for abso
lute truth and began instead to ask how things worked, modern science
was born. Curiously, it was by abandoning the search for absolute truth
that science began to make progress, opening the material universe
to human exploration. It was only by being provisional and open to
change, even radical change, that scientific knowledge began to evolve.
And ironically, its vulnerability to change is the source of its strength."
(From Perfect Symmetry: The Search for the Beginning of Time, Simon
and Schuster, New York 1985, p. 370).
It is evident that this work represents the fruits of collaboration among
many more individuals than the editors. Our special thanks go to the many
distinguished statisticians who replied to our inquiries, in many cases re
sponding to further "follow-up" letters requiring additional effort in provid
ing more details that we felt were desirable; we also would like to thank those
who have provided introductions to the chosen papers. The latter are ac
knowledged at the appropriate places where their contributions occur.
We take this opportunity to express our gratitude to Dean R.T. Lamone
of the College of Business and Professor B.L. Golden, Chairman of the De
partment of Management Science and Statistics at the University of Mary
land at College Park, and to Professor S. Cambanis, Chairman of the Depart
ment of Statistics at the University of North Carolina at Chapel Hill, for their
encouragement and the facilities they provided in support of our work on this
project.
We are also grateful to the various persons and organizations who have
given us reprint permission. They are acknowledged, together with source
references, in the section "Sources and Acknowledgments."