Page 641 - Probability and Statistical Inference

618 14. Appendix

1953. Since 1953, he has been a professor in the department of statistics at
Stanford University.
In an interview article [DeGroot (1986d)], Stein told that he had always
intended to be a mathematician. After studying some works of Wald, he pub-
lished the landmark paper [Stein (1945)] on a two-stage sampling strategy for
testing the mean of a normal population whose power did not depend on the
unknown population variance.
Stein received encouragement from senior researchers including A. Wald,
J. Neyman and K. J. Arrow. He started to generalize some of Wald’s work on
most stringent tests. In the interview article [DeGroot (1986d)], Stein men-
tioned that G. Hunt pointed it out to him that what he was doing was group
theory. He did not realize this in the beginning. Eventually, HuntStein Theorem
became a household phrase within the realm of invariance where Stein made
fundamental contributions.
Stein’s best known result is perhaps his proof of the inadmissibility [Stein
(1956)] of the sample mean vector as an estimator of the mean vector µ in
the N (µ, I) population when the dimension p is three or higher, under the
p
quadratic loss function. Later, James and Stein (1961) gave an explicit esti-
mator which had its risk smaller than that of , for all µ, under the quadratic
loss function. The dominating estimator has come to be known as the James-
Stein estimator. In this area, one frequently encounters a special identity which
is called the Stein Identity. James and Stein (1961) has been included in the
Breakthroughs in Statistics, Volume I [Johnson and Kotz (1992)]. Berger (1985)
gave an elegant exposition of this problem and its generalizations. DeGroot
(1986d) portrayed a delightful account of Stein’s life and career. Stein re-
mains busy and active in research.
“Student” (W. S. Gosset): William Sealy Gosset was born in 1876, the
oldest child of a Colonel in the Royal Engineers. He was a pioneer in the
development of statistical methods for design and analysis of experiments. He
is perhaps better known under the pseudonym “Student” than under his own
name. In most of his papers, he preferred to use the pseudonym “Student”
instead of his given name.
Following his father’s footsteps, Gosset entered the Royal Military Acad-
emy, Woollwich, to become a Royal Engineer himself. But, he was rejected
on account of poor eyesight. He graduated (1899) with a first class degree in
chemistry from New College in Oxford, and then joined the famous Guinness
Brewery in Dublin as a brewer. He stayed with this brewing firm for all his
life, ultimately becoming the Head Brewer in a new installation operated by the
Guinness family at Park Royal, London in 1935.
Gosset needed and developed statistical methods for small sample sizes
which he would then apply immediately to ascertain relationships between