## Girshick, Meyer A.

## Girshick, Meyer A.

# Girshick, Meyer A.

Meyer Abraham Girshick (1908–1955), American statistician, was born in Russia and immigrated to the United States in 1922. After graduating from Columbia College in 1932, he did graduate work in statistics under Harold Hotelling at Columbia University from 1934 until 1937. (Several years later he received a doctorate from Columbia.) In 1937-1939 he was a statistician with the Bureau of Home Economics, U.S. Department of Agriculture, where he participated in a pioneer study of body measurements of 147,000 American children that helped manufacturers to develop improved sizing of garments. At the same time, he gave evening courses in statistics at the U.S. Department of Agriculture Graduate School, courses that had a profound influence on the dissemination of sound statistical methods in government work and encouraged many new research workers. In 1939-1944 and again in 1945-1946 he was principal statistician for the Bureau of Agricultural Economics. For one year during World War ii he participated in the work of the Statistical Research Group at Columbia University, a panel composed of statisticians and designed to develop statistical methods appropriate to wartime problems. Working with others on the panel, particularly Abraham Wald, had a decisive influence on Girshick’s subsequent career. After a brief stay at the Bureau of the Census, he became a research statistician and mathematician at the RAND Corporation in Santa Monica, California (a research organization primarily devoted to work for the U.S. Air Force). From 1948 until his untimely death in 1955 he was professor of statistics at Stanford University. He was elected president of the Institute of Mathematical Statistics (one of the principal learned societies for theoretical statistics) in 1951.

His early papers, written between 1936 and 1944, were primarily concerned with problems of multivariate statistical analysis. His major achievement was to find the distribution of the roots and characteristic vectors associated with certain determinantal equations that are used in testing the null hypothesis that two sets of variates are inde pendent (1939). [*See*Multivariate analysis.]

Subsequently he also found the distribution of these roots when the null hypothesis is not true. From this the power function of certain tests can in principle be obtained (1941).

His interest in multivariate analysis and his substantive work at the Bureau of Agricultural Economics combined to turn his attention to newly developing methods of estimation of simultaneous equations in economics. These methods were originated by Trygve Haavelmo and continued by Tjalling Koopmans, T. W. Anderson, and Herman Rubin. In collaboration with Haavelmo, Girshick conducted one of the first major empirical studies on an econometric model for the agricultural sector of the United States economy (1947), and through unpublished work he contributed importantly to the development of the limited-information approach to simultaneous equation estimation. [*See*Simultaneous Equation Estimation.]

During the period that Girshick was associated with the Statistical Research Group, Wald was originating two major concepts of statistics: sequential analysis and statistical decision theory [*see*Decision theory; sequential analysis; *and the biography of*Wald]. Girshick’s subsequent work was almost exclusively confined to these two areas (see Blackwell & Girshick 1954).

His earliest work in sequential analysis concerned the testing of composite hypotheses in which the mean of one process is less than, or equal to, the mean of another, the alternative being that it is greater. He showed that the power functions of such tests were constant on certain curves in the parameter space, and he was able to use this information to derive approximate sequential tests for the parameters of the exponential family of distributions (1946a). He also found exact relations for tests when the variables take on only a finite set of values. As a by-product of his interest in sequential analysis he found, in collaboration with Frederick Mosteller and L. J. Savage, a method of getting unbiased estimates of a parameter from data that have been generated by a sequential, or similar, sampling scheme (Girshick et al. 1946*b*). He and David Blackwell found a lower bound for the variance of such estimates (Blackwell & Gir shick 1947).

His work in decision theory was developed in a series of papers, most of them coauthored with Blackwell, Rubin, Savage, or Arrow. The major results of these studies were systematically presented in *Theory of Games and Statistical Decisions* (1954), written jointly with Blackwell. This book today represents a major study of statistical method using the concepts of the theory of games from the decision-theory point of view. The theory of games, which is closely allied to decision theory, is also given prominence in the book. [*See*Game theory.] Among its most noteworthy accomplishments are a study of the interrelations of various criteria for complete classes of solutions and related concepts and a systematic treatment of Bayesian and related procedures in statistical contexts. Other special features include rigorous analysis of the concepts of sufficiency and of invariance, a clear exposition and characterization of sequential probability-ratio tests and their optimal properties, a study of Bayesian estimation procedures with special loss functions, particularly the quadratic and the absolute value, and the theory of comparison of experiments.

Girshick’s influence on the development of statistical theory occurred as much through his direct personal relations, his enthusiasm and intelligent guidance, as through his published work, important as the latter is.

Kenneth J. Arrow

## WORKS BY GIRSHICK

1939 On the Sampling Theory of Determinantal Equations. *Annals of Mathernatical Statistics* 10:203–224.

1941 The Distribution of the Ellipticity Statistic *L*_{o}, When the Hypothesis Is False. *Terrestrial Magnetism and Atmospheric Electricity* 46:455–457.

1946*a* Contributions to the Theory of Sequential Analysis. *Annals of Mathematical Statistics* 17:123-143, 282–298.

1946*b* Girshick, Meyer A.; Mosteller, Frederick; and Savage, L. J. Unbiased Estimates for Certain Binomial Sampling Problems With Applications. *Annals of Mathematical Statistics* 17:13–23.

1947 Girshick, Meyer A.; and Haavelmo, Trygve Statistical Analysis of the Demand for Food: Examples of Simultaneous Estimation of Structural Equations. *Econometrica* 15:79–110.

1947 Blackwell, David; and Girshick, Meyer A. A Lower Bound for the Variance of Some Unbiased Sequential Estimates. *Annals of Mathematical Statistics* 18:277–280.

1954 Blackwell, David; and Girshick, Meyer A. *The ory of Games and Statisticat Decisions.* New York: Wiley.

## SUPPLEMENTARY BIBLIOGRAPHY

Blackwell, David; and Bowker, Albert H. 1955 Meyer Abraham Girshick: 1908–1955. *Annals of Mathematical Statistics* 26:365–367.