233
Views
13
CrossRef citations to date
0
Altmetric
General

An Essay on Statistical Decision Theory

Pages 1277-1281 | Published online: 17 Feb 2012

References

  • Abramowich , F. and Benjamini , Y. 1995 . “Threshholding of Wavelet Coefficients as Multiple Testing Procedures,” . In Wavelets and Statistics , Edited by: Antoniadis , A. 5 – 14 . New York : Springer-Verlag .
  • Abramowich , A. , Benjamini , Y. , Donoho , D. and Johnstone , I. M. 1999 . “Sparsity and Threshholding via False Discovery Control,” preprint
  • Benjamini , Y. and Hochberg , Y. 1995 . “Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing” . Journal of the Royal Statistical Society , 57 : 289 – 300 . Ser. B
  • Berger , J. O. and Strawderman , W. E. 1996 . “Choice of Hierarchical Priors: Admissibility in Estimation of Normal Means” . The Annals of Statistics , 24 : 931 – 951 .
  • Bernardo , J. M. 1979 . “Reference Prior Distributions for Bayesian Inference” . Journal of the Royal Statistical Society , 41 : 113 – 147 . Ser. B
  • Brown , L. D. 1979 . “A Heuristic Method for Determining Admissibility of Estimators, With Applications” . The Annals of Statistics , 7 : 960 – 994 .
  • Brown , L. D. 1994 . “Minimaxity, More or Less,” . In Statistical Decision Theory and Related Topics , Edited by: Gupta , S. S. and Berger , J. O. 1 – 18 . New York : Springer-Verlag .
  • Brown , L. D. , Cai , T. T. and DasGupta , A. 1999a . “Interval Estimation for a Binomial Proportion,” submitted for publication
  • Brown , L. D. , Cai , T. T. and DasGupta , A. 1999b . “Confidence Intervals for a Binomial Proportion and Edgeworth Expansions,” submitted for publication
  • Brown , L. D. and Low , M. G. 1991 . “Information Inequality Bounds on the Minimax Risk With an Application to Nonparametric Regression” . The Annals of Statistics , 19 : 329 – 337 .
  • Brown , L. D. and Low , M. G. 1996 . “Asymptotic Equivalence of Nonparametric Regression and White Noise” . The Annals of Statistics , 24 : 2384 – 2398 .
  • Brown , L. D. , Low , M. G. and Zhao , L. H. 1997 . “Superefficiency in Nonparametric Function Estimation” . The Annals of Statistics , 25 : 2607 – 2625 .
  • Casella , G. and Strawderman , W. E. 1981 . “Estimating a Bounded Normal Mean” . The Annals of Statistics , 9 : 870 – 878 .
  • Clopper , C. J. and Pearson , E. S. 1934 . “The Use of Confidence or Fiducial Limits Illustrated in the Case of the Binomial” . Biometrika , 26 : 404 – 413 .
  • Donoho , D. L. 1994 . “Statistical Estimation and Optimal Recovery” . The Annals of Statistics , 22 : 238 – 270 .
  • Donoho , D. L. and Johnstone , I. M. 1995 . “Adapting to Unknown Smoothness via Wavelet Shrinkage” . Journal of the American Statistical Association , 90 : 1200 – 1224 .
  • Donoho , D. L. and Johnstone , I. M. 1998 . “Minimax Estimation via Wavelet Shrinkage” . The Annals of Statistics , 26 : 879 – 921 .
  • Donoho , D. L. and Liu , R. C. 1991 . “Geometrizing Rates of Convergence III” . The Annals of Statistics , 19 : 668 – 701 .
  • Donoho , D. L. , Liu , R. C. and MacGibbon , B. 1990 . “Minimax Risk for Hyperrectangles” . The Annals of Statistics , 18 : 1416 – 1437 .
  • Eaton , M. L. 1992 . “A Statistical Diptych: Admissible Inferences–Recurrence of Symmetric Markov Chains” . The Annals of Statistics , 20 : 1147 – 1179 .
  • Efron , B. 1998 . “R. A. Fisher in the 21st Century” . Statistical Science , 13 : 95 – 113 . (with discussion)
  • Hodges , J. L. Jr. and Lehmann , E. L. 1950 . “The Use of Previous Experience in Reaching Statistical Decisions” . Annals of Mathematical Statistics , 23 : 396 – 407 .
  • Hodges , J. L. Jr. and Lehmann , E. L. “Some Applications of the Cramer–Rao Inequality,” . Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability . Vol. 1 , pp. 13 – 22 . Berkeley , CA : University of California Press .
  • James , W. and Stein , C. “Estimation With Quadratic Loss,” . Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability . Vol. 1 , pp. 311 – 319 . Berkeley , CA : University of California Press .
  • Jennison , C. and Turnbull , B. W. 1990 . “Statistical Approaches to Interim Monitoring of Medical Trials: A Review and Commentary” . Statistical Science , 5 : 299 – 317 .
  • Johnstone , I. M. “False Discovery Rates and Adaptive Estimation” . Special invited paper presented at the 1999 Joint Statistical Meetings in Baltimore .
  • Kolmogorov , A. 1933 . “Sulla Determinazione Empirica di una Leggi di Distribuzione” . Giornale dell'Instituto Italiana degli Attuari , 4 : 83 – 91 .
  • Le Cam , L. 1953 . On Some Asymptotic Properties of Maximum Likelihood Estimates and Related Bayes Procedures , 277 – 230 . Berkeley , CA : University of California Press .
  • Le Cam , L. 1964 . “Sufficiency and Approximate Sufficiency” . Annals of Mathematical Statistics , 35 : 1419 – 1455 .
  • Le Cam , L. 1986 . Asymptotic Methods in Statistical Decision Theory , New York : Springer-Verlag .
  • Lehmann , E. L. and Casella , G. 1998 . Theory of Point Estimation, , 2nd ed. , New York : Springer .
  • Neyman , J. 1935 . “On the Problem of Confidence Intervals” . Annals of Mathematical Statistics , 6 : 111 – 116 .
  • Neyman , J. 1941 . “Fiducial Argument and the Theory of Confidence Intervals” . Biometrika , 32 : 128 – 150 .
  • Neyman , J. “Contribution to the Theory of the Chi-Square Test,” . Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability . pp. 239 – 273 . Berkeley , CA : University of California Press .
  • Neyman , J. Lectures and Conferences on Mathematical Statistics and Probability . Washington , D.C. : U.S. Department of Agriculture .
  • Neyman , J. 1967 . A Selection of Early Statistical Papers of J. Neyman , Berkeley , CA : University of California Press .
  • Neyman , J. and Pearson , E. S. 1933 . “The Testing of Statistical Hypotheses in Relation to Probabilities a Priori” . Proceedings of the Cambridge Philosophical Society , 29 : 492 – 510 .
  • Nussbaum , M. 1996 . “Asymptotic Equivalence of Density Estimation and Gaussian White Noise” . The Annals of Statistics , 24 : 2399 – 2430 .
  • Parzen , E. 1962 . “On the Estimation of a Probability Density and Mode” . Annals of Mathematical Statistics , 33 : 1065 – 1076 .
  • Rosenblatt , M. 1956 . “Remarks on Some Nonparametric Estimates of a Density Function” . Annals of Mathematical Statistics , 27 : 832 – 837 .
  • Siegmund , D. 1994 . “A Retrospective of Wald's Sequential Analysis–Its Relation to Changepoint Detection and Sequential Clinical Trials,” . In Statistical Decision Theory and Related Topics , Edited by: Gupta , S. S. and Berger , J. O. 19 – 33 . New York : Springer-Verlag .
  • Smirnov , N. V. 1939 . “On the Estimation of the Discrepancy Between Empirical Curves of Distributions for Two Independent Samples” . Bulletin of the University of Moscow , 2 ( 2 ) : 3 – 14 .
  • Stein , C. “Efficient Nonparametric Testing and Estimation,” . Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability . pp. 187 – 196 . Berkeley , CA : University of California Press .
  • Stein , C. “Inadmissibility of the Usual Estimator for the Mean of a Multivariate Normal Distribution,” . Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability . pp. 197 – 206 . Berkeley , CA : University of California Press .
  • Stein , C. “Estimation of the Mean of a Multivariate Distribution,” . Proceedings of the Prague Symposium on Asymptotic Statistics . pp. 345 – 381 .
  • Stein , C. 1981 . “Estimation of the Mean of a Multivariate Normal Distribution” . The Annals of Statistics , 9 : 1135 – 1151 .
  • Wald , A. 1939 . “Contributions to the Theory of Statistical Estimation and Testing Hypotheses” . Annals of Mathematical Statistics , 10 : 299 – 326 .
  • Wald , A. 1942 . On the Principles of Statistical Inference Notre Dame , IN
  • Wald , A. 1943 . “Tests of Statistical Hypotheses Concerning Several Parameters When the Number of Observations is Large” . Transactions of the American Mathematical Society , 54 : 426 – 482 .
  • Wald , A. 1947 . Sequential Analysis , New York : Wiley .
  • Wald , A. 1950 . Statistical Decision Functions , New York : Wiley .
  • Wald , A. and Wolfowitz , J. 1939 . “Confidence Limits for a Continuous Distribution Function” . Annals of Mathematical Statistics , 10 : 105 – 118 .
  • Wald , A. and Wolfowitz , J. 1941 . “Note on Confidence Limits for Continuous Distribution Functions” . Annals of Mathematical Statistics , 12 : 118 – 119 .
  • Wald , A. and Wolfowitz , J. 1950 . “Bayes Solution of Sequential Decision Problems” . Annals of Mathematical Statistics , 21 : 82 – 89 .
  • Wilson , E. B. 1927 . “Probable Inference, the Law of Succession, and Statistical Inference” . Journal of the American Statistical Association , 22 : 209 – 212 .
  • Zhao , L. H. 1999 . “Improved Estimators in Nonparametric Regression Problems” . Journal of the American Statistical Association , 94 : 164 – 173 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.