On the Non-Optimality of Optimal Procedures

This paper discusses some subtle, and largely overlooked, differences between conceptual and mathematical optimization goals in statistics, and illustrates them by examples.

[1]  R. Fisher A mathematical Examination of the Methods of determining the Accuracy of Observation by the Mean Error, and by the Mean Square Error , 1920 .

[2]  E. L. Lehmann,et al.  Theory of point estimation , 1950 .

[3]  Stephen E. Fienberg,et al.  Testing Statistical Hypotheses , 2005 .

[4]  F. Hampel Contributions to the theory of robust estimation , 1968 .

[5]  Robert L. Wolpert A Conversation with James O. Berger , 2004 .

[6]  D. Freedman,et al.  On The So-Called “Huber Sandwich Estimator” and “Robust Standard Errors” , 2006 .

[7]  P. J. Huber APPLICATIONS VS. ABSTRACTION: THE SELLING OUT OF MATHEMATICAL STATISTICS? , 1975 .

[8]  C. Jennison,et al.  Robust Statistics: The Approach Based on Influence Functions , 1987 .

[9]  W. Näther Optimum experimental designs , 1994 .

[10]  K. Menninger On war. , 1973, Bulletin of the Menninger Clinic.

[11]  P. J. Huber A Robust Version of the Probability Ratio Test , 1965 .

[12]  P. Rousseeuw Least Median of Squares Regression , 1984 .

[13]  Werner A. Stahel,et al.  Robust Statistics: The Approach Based on Influence Functions , 1987 .

[14]  G. Box,et al.  A Basis for the Selection of a Response Surface Design , 1959 .

[15]  E. S. Pearson,et al.  On the Problem of the Most Efficient Tests of Statistical Hypotheses , 1933 .

[16]  R. Viertl On the Future of Data Analysis , 2002 .

[17]  P. J. Huber Robust confidence limits , 1968 .

[18]  H. Rieder Robust asymptotic statistics , 1994 .

[19]  F. Hampel The Influence Curve and Its Role in Robust Estimation , 1974 .

[20]  G. Box NON-NORMALITY AND TESTS ON VARIANCES , 1953 .

[21]  D. Freedman On the Asymptotic Behavior of Bayes' Estimates in the Discrete Case , 1963 .

[22]  Peter J. Rousseeuw,et al.  ROBUST REGRESSION BY MEANS OF S-ESTIMATORS , 1984 .

[23]  Kuldeep Kumar,et al.  Robust Statistics, 2nd edn , 2011 .

[24]  Le Cam,et al.  On some asymptotic properties of maximum likelihood estimates and related Bayes' estimates , 1953 .

[25]  Abraham Wald,et al.  Statistical Decision Functions , 1951 .

[26]  H. P. Stellar Movements and the Structure of the Universe , 1915, Nature.

[27]  C. Huber-Carol Etude asymptotique de tests robustes , 1970 .

[28]  C. Stein,et al.  Estimation with Quadratic Loss , 1992 .

[29]  Le Cam,et al.  Locally asymptotically normal families of distributions : certain approximations to families of distributions & thier use in the theory of estimation & testing hypotheses , 1960 .

[30]  P. L. Davies Aspects of Robust Linear Regression , 1993 .

[31]  Frederick R. Forst,et al.  On robust estimation of the location parameter , 1980 .