Studies in Econometrics, Time Series, and Multivariate Statistics

565 Pages·1983·20.661 MB·English

by  Samuel Karlin

THEODORE W. ANDERSON
Studies in Econometrics, Time Series,
and Multivariate Statistics
EDITED BY
SAMUEL KARLIN
Department of Mathematics
Stanford University
Stanford, California
TAKESHI AMEMIYA
Department of Economics
Stanford University
Stanford, California
LEO A. GOODMAN
Departments of Statistics and Sociology
University of Chicago
Chicago, Illinois
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Library of Congress Cataloging in Publication Data
Main entry under title:
Studies in econometrics, time series, and multivariate
statistics·
"In commemoration of T.W. Anderson's 65th birthday."
Includes bibliograpical references.
1. Econometrics—Addresses, essays, lectures.
2. Time-series analysis—Addresses, essays, lectures.
3. Multivariate analysis—Addresses, essays, lectures.
4. Social sciences—Statistical methods—Addresses,
essays, lectures. 5. Anderson, T. W. (Theodore Wilbur),
Date · I. Karlin, Samuel, Date
II. Amemiya, Takeshi. III. Goodman, Leo A. IV. Ander-
son, T. W. (Theodore Wilbur), Date
HB139.S83 1983 330'.028 83-15523
ISBN 0-12-398750-4
PRINTED IN THE UNITED STATES OF AMERICA
88 89 90 91 92 10 9 8 7 6 5 4 3
Contributors
Numbers in parentheses indicate the pages on which the authors' contributions begin.
TAKESHI AMEMIYA (3), Department of Economics, Stanford University,
Stanford, California 94305
DAVID R. BRILLÏNGER (31), Department of Statistics, University of
California, Berkeley, California 94720
B. W. BROWN (131), Department of Economics, Princeton University,
Princeton, New Jersey 08544
ARTHUR COHEN (379), Department of Statistics, Rutgers University, New
Brunswick, New Jersey 08903
SOMESH DAS GUPTA (407), School of Statistics, University of Minnesota,
Minneapolis, Minnesota 55455
J. DURBIN (243), Department of Statistical and Mathematical Sciences, The
London School of Economics and Political Sciences, London, England
C. FANG (419), Center for Multivariate Analysis, University of Pittsburgh,
Pittsburgh, Pennsylvania 15260
CONSTANTINE GATSONIS (379), Department of Statistics, Rutgers
University, New Brunswick, New Jersey 08903
ARTHUR S. GOLDBERGER (67), Department of Economics, University of
Wisconsin, Madison, Wisconsin 53706
LEO A. GOODMAN (85), Departments of Statistics and Sociology,
University of Chicago, Chicago, Illinois 60637
C. W. J. GRANGER (255), Department of Economics, University of
California at San Diego, La Jolla, California 92093
ix
X Contributors
LARRY V. HEDGES (437), Department of Education, University of Chicago,
Chicago, Illinois 60637
CHENG HSIAO (93), Institute for Policy Analysis, University of Toronto,
Toronto, Ontario M5S 1A1, Canada
A. T. JAMES (455), Department of Statistics, University of Adelaide,
Adelaide, South Australia 5001
SAMUEL KARLIN (465), Department of Mathematics, Stanford University,
Stanford, California 94305
P. R. KRISHNAIAH (419), Center for Multivariate Analysis, University of
Pittsburgh, Pittsburgh, Pennsylvania 15260
E. L. LEHMANN (491), Department of Statistics, University of California,
Berkeley, California 94720
JOHN MARDEN (379), Department of Mathematics, University of Illinois,
Urbana, Illinois 61801
ROBERTO S. MARIANO (131), Department of Economics, University of
Pennsylvania, Philadelphia, Pennsylvania 19104
INGRAM OLKIN (437), Department of Statistics, Stanford University,
Stanford, California 94305
EMANUEL PARZEN (279), Institute of Statistics, Texas A & M University,
College Station, Texas 77843
MICHAEL D. PERLMAN (505), Department of Statistics, University of
Washington, Seattle, Washington 98195
JAMES L. POWELL (3), Department of Economics, Massachusetts Institute of
Technology, Cambridge, Massachusetts 02139
HAIGANOUSH K. PREISLER (31), Northern California Sickle Cell Center,
University of California at San Francisco, San Francisco, California 94117
C. R. RAO (529), Center for Multivariate Analysis, University of
Pittsburgh, Pittsburgh, Pennsylvania 15260
YOSEFRINOTT (465), Department of Statistics, Hebrew University of
Jerusalem, Jerusalem 91905, Israel
MURRAY ROSENBLATT (299), Department of Mathematics, University of
California at San Diego, La Jolla, California 92093
THOMAS J. ROTHENBERG (153), Department of Economics, University of
California, Berkeley, California 94720
J. D. SARGAN (169), Department of Economics, London School of
Economics and Political Science, London, England
Contributors xi
STANLEY L. SCLOVE (311), Quantitative Methods Department, College of
Business Administration, University Center, University of Illinois,
Chicago, Illinois 60680
PAUL SHAMAN (331), Department of Statistics, The Wharton School,
University of Pennsylvania, Philadelphia, Pennsylvania 19104
GEORGE P. H. STYAN (545), Department of Mathematics, McGill
University, Montreal, Quebec, Canada
AKIMICHI TAKEMURA (545), Department of Statistics, Stanford University,
Stanford, California 94305
JOHN B. TAYLOR (207), Department of Economics, Princeton University,
Princeton, New Jersey 08544
A. M. WALKER (343), Department of Probability and Statistics, The
University of Sheffield, Sheffield S3 74H, England
G. S. WATSON (559), Department of Statistics, Princeton University,
Princeton, New Jersey 08544
A. A. WEISS (255), Department of Economics, University of California at
San Diego, La Jolla, California 92093
ARNOLD ZELLNER (227), Graduate School of Business, University of
Chicago, Chicago, Illinois 60637
Biographical Note
In commemoration of Ted Anderson's 65th birthday, his many friends,
students, and scientific associates offer him their affection, esteem, and best
wishes for everlasting good health and for continued discoveries of statistical
and econometric significance. The contributions of this Festschrifi, centering
on the themes of multivariate statistical analysis, time series processes, econ-
ometrics, and quantitative social science studies, attest to the importance and
influence of T. W. Anderson's scholarship and research (see attached bibli-
ography).
Born on June 5, 1918, in Minneapolis, Minnesota, Anderson studied at
North Park College and received his B.S. from Northwestern University in
1939 and his Ph.D. from Princeton University in 1945. He participated actively
in the research program of the Cowles Commission for Research in Eco-
nomics at the University of Chicago in 1945-1946, and from there went on to
Columbia University as an instructor in mathematical statistics in 1946, rising
through the ranks to full professor by 1956. He moved to his present position
at Stanford as Professor of Statistics and Economics in 1967. Anderson has
been recognized in many ways during his distinguished career. He serves on
the editorial boards of many international scientific journals. He is a member
of the International Statistical Institute, a fellow of the Institute of Mathemat-
ical Statistics (President, 1962-1963), a fellow of the American Statistical Asso-
ciation (Vice-President, 1971-1973), a fellow of the Econometric Society; and
he was elected to the American Academy of Arts and Sciences in 1974 and to
the National Academy of Sciences in 1976.
Anderson's early work pioneered a number of "non-null" distributions, for
which he derived explicit forms of the noncentral Wishart distribution (over-
lapping some independent results of M. A. Girshick). These results are fun-
damental to the development of essential statistical theory for characteristic
roots and vectors of covariance matrices and related quantities (for tests, esti-
mates, asymptotic distributions, and confidence regions). Anderson's work
xiii
XIV Biographical Note
has found immediate applications in econometrics in terms of the Limited
Information Maximum Likelihood estimate for every single equation in a sys-
tem. This method and its subsequent simplification (by Theil and Basmann)
have played an important role in estimating simultaneous equation models in
economics. Anderson has recently published many results concerning the ex-
act and approximate distributions of these estimators and their subsequent
modifications.
Anderson has also concentrated on developing inference procedures for
covariance matrices that are linear combinations of known matrices. He dis-
covered that the probability of a convex symmetric set decreases as the center
of the set departs along a ray from the center for a symmetric unimodal
density; this result supports a broad hierarchy of basic inequalities for multi-
variate distributions.
His work on time series analysis extended and applied the basic Neyman-
Pearson theory to tests of independence and order of dependence for time
series. Recent papers present methods for general autoregressive moving aver-
age models.
Anderson's work has also had a substantial influence on quantitative psy-
chology and sociology. He wrote (with Herman Rubin) the first comprehen-
sive treatment of statistical inference in factor analysis, introducing new con-
cepts and methods. Later papers dealt incisively with problems in ''scaling"
and "measurement."
In evaluating T. W. Anderson's many outstanding and versatile contribu-
tions to statistical and econometric theory, we would be remiss in not high-
lighting his masterful text, An Introduction to Multivariate Statistical Analysis (an
updated revised edition is in the works), which is among the most frequently
cited works in the statistical literature and which has been widely applied
throughout the sciences.
Samuel Karlin
Takeshi Amemiya
Leo Goodman
May 1, 1983
Bibliography of Theodore W. Anderson
Books
1. "An Introduction to Multivariate Statistical Analysis," 374 pp. Wiley, New York (1958).
[Russian translation: Vvedenie v Mnogomernyi Statisticeskii Analiz, 500 pp. Gosudarstvennoe
Izdatel'stvo Fiziko-matematiceskoi Literatury, Moscow (1963).]
2. "The Statistical Analysis of Time Series," 704 pp. Wiley, New York (1971). [Russian trans-
lation: Statisticeskii Analiz Vremennykh Rjadov, 755 pp. Izdatelstvo MIR, Moscow (1976).]
3. "A Bibliography of Multivariate Statistical Analysis (with S. Das Gupta and G. P. H. Styan)
642 pp. Oliver & Boyd, Edinburgh, and Halsted Press (1972). [Reprinted, Robert E.
Krieger, Huntington, New York (1977).]
4. "Introductory Statistical Analysis" (with Stanley L. Sclove), 499 pp. Houghton Mifflin,
Boston (1974).
5. "An Introduction to the Statistical Analysis of Data" (with Stanley L. Sclove), 704 pp.
Houghton Mifflin, Boston (1978).
Papers
1. Some significance tests for normal bivariate distributions (with D. S. Villars). Annals of
Mathematical Statistics 14, 141-148 (1943).
2. On card matching. Annals of Mathematical Statistics 14, 426-435 (1943).
3. Some extensions of the Wishart distribution (with M. A. Girshick). Annals of Mathematical
Statistics 15, 345-357 (1944). [Correction 35, 923-924 (1964).]
4. The non-central Wishart distribution and certain problems of multivariate statistics. Annals of
Mathematical Statistics 17, 409-431 (1946). (Correction 35, 923-924 (1964).]
5. A note on a maximum-likelihood estimate. Econometrica 15, 241-244 (1947).
6. On the theory of testing serial correlation. Skandinavisk Aktuarietidskrifi 31, 88-116 (1948).
7. The asymptotic distributions of the roots of certain determinantal equations. Journal of the
Royal Statistical Society, Ser. B 10, 132-139 (1948).
8. Estimation of the parameters of a single equation in a complete system of stochastic equa-
tions (with Herman Rubin). Annals of Mathematical Statistics 20, 46-63 (1949). [Reprinted in
"Readings in Econometric Theory" (J. Malcolm Dowling and Fred R. Glahe, eds.), Colora-
do Associated University Press, pp. 358-375 (1970).]
9. Distribution of the circular serial correlation coefficient for residuals from a fitted Fourier
series (with R. L. Anderson). Annals of Mathematical Statistics 21, 59-81 (1950).
10. Estimation of the parameters of a single equation by the limited-information maximum-
likelihood method. In "Statistical Inference in Dynamic Economic Models" (Tjalling C.
Koopmans, ed.), pp. 311-322. Wiley, New York (1950).
xv
XVI Bibliography
11. The asymptotic properties of estimates of the parameters of a single equation in a complete
system of stochastic equations (with Herman Rubin). Annals of Mathematical Statistics 21,
570-582 (1950). [Reprinted in "Readings in Econometric Theory" (J. Malcolm Dowling and
Fred R. Glahe, eds.). Colorado Associated University Press, pp. 376-388 (1970).]
12. Classification by multivariate analysis. Psychometrika 16, 31-50 (1951).
13. The asymptotic distribution of certain characteristic roots and vectors. In "Proceedings of
the Second Berkeley Symposium on Mathematical Statistics and Probability" (Jerzy Ney-
man, ed.), pp. 105-130. Univ. California Press, Berkeley, California (1951).
14. Estimating linear restrictions on regression coefficients for multivariate normal distributions.
Annals of Mathematical Statistics 22, 327-351 (1951). [Correction, Annals of Statistics 8, 1400
(1980.)]
15. Asymptotic theory of certain "goodness of fit" criteria based on stochastic processes (with
D. A. Darling). Annals of Mathematical Statistics 23, 193-212 (1952).
16. Probability models for analyzing time changes in attitudes. In "Mathematical Thinking in
the Social Sciences" (Paul F. Lazarsfeld, ed.), pp. 17-66. The Free Press, Glencoe, Illinois
(1954).
17. On estimation of parameters in latent structure analysis. Psychometrika 19, 1-10 (1954).
18. A test of goodness of fit (with D. A. Darling). Journal of the American Statistical Association 49,
765-769 (1954).
19. Some statistical problems in relating experimental data to predicting performance of a pro-
duction process. Journal of the American Statistical Association 50, 163-177 (1955).
20. The integral of a symmetric unimodal function over a symmetric convex set and some
probability inequalities. Proceedings of the American Mathematical Society 6, 170-176 (1955).
21. Department of Mathematical Statistics. In "History of the Faculty of Political Science." pp.
250-255. Columbia Univ. Press, New York (1955).
22. Some recent results in latent structure analysis. In "Proceedings of the Invitational Confer-
ence on Testing Problems, October 30, 1954," pp. 49-53. Educational Testing Service,
Princeton, New Jersey (1955).
23. Statistical inference in factor analysis (with Herman Rubin). In "Proceedings of the Third
Berkeley Symposium on Mathematical Statistics and Probability" (Jerzy Neyman, ed.),
Vol. 5, pp. 111-150. Univ. California Press, Berkeley, California (1956).
24. Statistical inference in Markov chains (with Leo A. Goodman). Annals of Mathematical Statis-
tics 28, 89-110 (1957). [Reprinted in "Readings in Mathematical Psychology" (R. Duncan
Luce, Robert R. Bush, and Eugene Galanter, eds.), Vol. 1, pp. 241-262. Wiley, New York
(1963).]
25. Maximum likelihood estimates for a multivariate normal distribution when some observa-
tions are missing. Journal of the American Statistical Association 52, 200-203, (1957).
26. On asymptotic distributions of estimates of parameters of stochastic difference equations.
Annals of Mathematical Statistics 30, 676-687 (1959).
27. Some scaling models and estimation procedures in the latent class model. In "Probability and
Statistics: The Harald Cramer Volume" (Ulf Grenander, ed.), pp. 9-38. Almqvist and
Wiksell, Stockholm (1959).
28. A modification of the sequential probability ratio test to reduce the sample size. Annals of
Mathematical Statistics 31, 165-197 (1960).
29. Harold Hotelling's research in statistics. The American Statistician 14, 17-21 (1960).
30. A limitation of the optimum property of the sequential probability ratio test (with Milton
Friedman). In "Contributions to Probability and Statistics; Essays in Honor of Harold
Hotelling" (Ingram Olkin, Sudhish G. Ghurye, Wassily Hoeffding, William G. Madow, and
Henry B. Mann, eds.), pp. 57-69. Stanford Univ. Press, Stanford, California (1960).
31. Some stochastic process models for intelligence test scores. In "Mathematical Methods in the
Social Sciences" (Kenneth J. Arrow, Samuel Karlin, and Patrick Suppes, eds.), pp. 205-220.
Stanford Univ. Press, Stanford, California (1960).
32. The choice of the degree of a polynomial regression as a multiple decision problem. Annals of
Mathematical Statistics 33, 255-265 (1962).