Charles Stein (statistician)
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Charles Max Stein (March 22, 1920 – November 24, 2016) was an American mathematical statistician and professor of statistics at Stanford University. He received his Ph.D in 1947 at
Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manha ...
with advisor
Abraham Wald Abraham Wald (; hu, Wald Ábrahám, yi, אברהם וואַלד;  – ) was a Jewish Hungarian mathematician who contributed to decision theory, geometry, and econometrics and founded the field of statistical sequential analysis. One o ...
. He held faculty positions at Berkeley and the
University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...
before moving permanently to Stanford in 1953. He is known for Stein's paradox in
decision theory Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical ...
, which shows that
ordinary least squares In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the ...
estimates can be uniformly improved when many parameters are estimated; for
Stein's lemma Stein's lemma, named in honor of Charles Stein, is a theorem of probability theory that is of interest primarily because of its applications to statistical inference — in particular, to James–Stein estimation and empirical Bayes methods ...
, giving a formula for the
covariance In probability theory and statistics, covariance is a measure of the joint variability of two random variables. If the greater values of one variable mainly correspond with the greater values of the other variable, and the same holds for the le ...
of one
random variable A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the p ...
with the value of a function of another when the two random variables are jointly normally distributed; and for
Stein's method Stein's method is a general method in probability theory to obtain bounds on the distance between two probability distributions with respect to a probability metric. It was introduced by Charles Stein, who first published it in 1972, to obtain a ...
, a way of proving theorems such as the
Central Limit Theorem In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables thems ...
that does not require the variables to be independent and identically distributed. He was a member of the
National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nat ...
. He died in November 2016 at the age of 96.


Works

*''Approximate Computation of Expectations'', Institute of Mathematical Statistics, Hayward, CA, 1986. * A bound for the error in the normal approximation to the distribution of a sum of dependent random variables, Sixth Berkeley Stanford Symposium, pages 583-602.


Interviews

* *


References

*
National University of Singapore Program Honoring Prof. SteinPhotograph of SteinAnother photograph


See also

*
James–Stein estimator The James–Stein estimator is a biased estimator of the mean, \boldsymbol\theta, of (possibly) correlated Gaussian distributed random vectors Y = \ with unknown means \. It arose sequentially in two main published papers, the earlier version o ...
*
Stein's lemma Stein's lemma, named in honor of Charles Stein, is a theorem of probability theory that is of interest primarily because of its applications to statistical inference — in particular, to James–Stein estimation and empirical Bayes methods ...
*
Stein's method Stein's method is a general method in probability theory to obtain bounds on the distance between two probability distributions with respect to a probability metric. It was introduced by Charles Stein, who first published it in 1972, to obtain a ...
*
Stein's unbiased risk estimate In statistics, Stein's unbiased risk estimate (SURE) is an unbiased estimator of the mean-squared error of "a nearly arbitrary, nonlinear biased estimator." In other words, it provides an indication of the accuracy of a given estimator. This is im ...
* Stein's loss *
Stein discrepancy A Stein discrepancy is a statistical divergence between two probability measures that is rooted in Stein's method. It was first formulated as a tool to assess the quality of Markov chain Monte Carlo samplers,J. Gorham and L. Mackey. Measuring Sam ...
1920 births 2016 deaths American mathematicians Columbia University alumni Members of the United States National Academy of Sciences Stanford University Department of Statistics faculty University of California, Berkeley faculty University of Chicago faculty Mathematical statisticians {{US-statistician-stub