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Bradley Efron


Bradley Efron

Bradley Efron
Born (1938-05-24) May 24, 1938
Nationality American
Fields Statistics
Institutions Stanford University
Alma mater California Institute of Technology, Stanford University
Thesis Problems in Probability of a Geometric Nature (1964)
Doctoral advisor Rupert Miller
Herbert Solomon
Doctoral students Norman Breslow
Robert Tibshirani
Known for Bootstrap method
Notable awards National Medal of Science (2005)

Bradley Efron (born May 24, 1938)[1] is an American statistician best known for proposing the bootstrap resampling technique,[2] which has had a major impact in the field of statistics and virtually every area of statistical application. The bootstrap was one of the first computer-intensive statistical techniques, replacing traditional algebraic derivations with data-based computer simulations.[3]


  • Life and career 1
  • Awards 2
  • Works 3
  • See also 4
  • References 5
  • External links 6

Life and career

Efron was born in St. Paul, Minnesota in May 1938, the son of Russian Jewish immigrants Esther and Miles Efron.[4] He attended the California Institute of Technology, graduating in Mathematics in 1960. He arrived at Stanford in fall of 1960, earning his Ph.D., under the direction of Rupert Miller and Herb Solomon, in the Department of Statistics. While at Stanford, he was suspended for a year for his involvement with the Stanford Chaparral's parody of Playboy magazine.[5][6]

He is currently a Professor of Statistics and Biostatistics at Stanford. At Stanford he has been the Chair of the Department of Statistics, Associate Dean of the School of Humanities and Sciences, Chairman of the University Advisory Board, Chair of the Faculty Senate and Co-director of the undergraduate-level Mathematical & Computational Science Program.

Efron holds the Max H. Stein endowed chair as Professor of Humanities and Sciences at Stanford.

He has made many important contributions to many areas of statistics. Efron's work has spanned both theoretical and applied topics, including empirical Bayes analysis (with Carl Morris), applications of differential geometry to statistical inference, the analysis of survival data, and inference for microarray gene expression data.[7] He is the author of a classic monograph, The Jackknife, the Bootstrap and Other Resampling Plans (1982) and has also co-authored (with R. Tibshirani) the text An Introduction to the Bootstrap (1994).

He created a set of nontransitive dice called Efron's dice.


He has won many honors, including a MacArthur Prize Fellowship, membership in the National Academy of Sciences and the American Academy of Arts and Sciences, fellowship in the Institute of Mathematical Statistics (IMS) and the American Statistical Association (ASA), the Lester R. Ford Award,[8] the Wilks Medal, the Parzen Prize, and the Rao Prize, Fisher, Rietz and Wald lecturer.[9]

In 2005, he was awarded the National Medal of Science, the highest scientific honor by the United States, for his exceptional work in the field of Statistics (especially for his inventing of the bootstrapping methodology).[10] He was presented with the award on May 29, 2007.[11]


  • Efron, B.;  
  • Bradley Efron (1979). "Bootstrap Methods: Another Look at the Jackknife".  
  • Bradley Efron;  
  • Efron, B. (1979). "Computer and the theory of statistics: thinking the unthinkable". SIAM Review.
  • Efron, B. (1981). "Nonparametric estimates of standard error: The jackknife, the bootstrap and other methods". Biometrika, 68, 589-599.
  • Efron, B. (1982). "The jackknife, the bootstrap, and other resampling plans". Society of Industrial and Applied Mathematics CBMS-NSF Monographs, 38.
  • Diaconis, P. & Efron, B. (1983). "Computer-intensive methods in statistics". Scientific American, May, 116-130.
  • Efron, B. (1983). "Estimating the error rate of a prediction rule: improvement on cross-validation". Journal of the American Statistical Association
  • Efron, B. (1985). "Bootstrap confidence intervals for a class of parametric problems." Biometrika.
  • Efron, B. (1987). "Better bootstrap confidence intervals". Journal of the American Statistical Association
  • Efron, B. (1990). "More efficient bootstrap computations". Journal of the American Statistical Association
  • Efron, B. (1991). "Regression precentiles using asymmetric squared error loss". Statistica sinica.
  • Efron, B. (1992). "Jackknife-after-bootstrap standards errors and influence functions". in Journal of the Royal Statistical Society
  • Efron, B., & Tibshirani, R. J. (1993). "An introduction to the bootstrap". New York: Chapman & Hall, software.

See also


  1. ^ Bradley Efron Curriculum Vitae
  2. ^ "Bootstrap Methods: Another Look at the Jackknife". Annals of Statistics Volume 7, Number 1, pages 1-26. 
  3. ^ Efron, Bradley (2013). "A 250-year argument: Belief, behavior, and the bootstrap". Bull. Amer. Math. Soc. (N.S.) 50 (1): 129–146.  
  4. ^
  5. ^ "Guide to the Hammer and Coffin Society Records, 1906-1987". Online Archive of California. 
  6. ^ "Bradley Efron". Significance, the bimonthly magazine and website of the Royal Statistical Society and the American Statistical Association. 
  7. ^ Bradley Efron (2010). Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing, and Prediction. Institute of Mathematical Statistics Monographs/Cambridge University Press.  
  8. ^ Efron, Bradley (1978). "Controversies in the Foundations of Statistics". Amer. Math. Monthly 85: 231–246.  
  9. ^ Awards - Special Lectures Info, Institute of Mathematical Statistics
  10. ^ National Science Foundation - The President's National Medal of Science
  11. ^

External links

  • Personal home page:
  • Statistical Science Silver Anniversary issue on Bootstrap, including interview with Efron
  • Bradley Efron at the Mathematics Genealogy Project
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