Charles Max Stein (March 22, 1920 – November 24, 2016) was an American mathematical statistician and professor of

statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

Stanford University Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is consider ...

. 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 Manhatt ...

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 of ...

. He held faculty positions at

Berkeley Berkeley most often refers to: *Berkeley, California, a city in the United States **University of California, Berkeley, a public university in Berkeley, California * George Berkeley (1685–1753), Anglo-Irish philosopher Berkeley may also refer ...

and the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...

before moving permanently to Stanford in 1953. He is known for

Stein's paradox In decision theory and estimation theory, Stein's example (also known as Stein's phenomenon or Stein's paradox) is the observation that when three or more parameters are estimated simultaneously, there exist combined estimators more accurate on av ...

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 prin ...

estimates can be uniformly improved when many parameters are estimated; for Stein's lemma, 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 les ...

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 po ...

with the value of a function of another when the two random variables are jointly normally distributed; and for Stein's method, 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 themselv ...

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 Nati ...

. 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

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

Works

Interviews

References

See also