论文信息 - Data Analysis Using Stein's Estimator and its Generalizations

Data Analysis Using Stein's Estimator and its Generalizations

Abstract In 1961, James and Stein exhibited an estimator of the mean of a multivariate normal distribution having uniformly lower mean squared error than the sample mean. This estimator is reviewed briefly in an empirical Bayes context. Stein's rule and its generalizations are then applied to predict baseball averages, to estimate toxomosis prevalence rates, and to estimate the exact size of Pearson's chi-square test with results from a computer simulation. In each of these examples, the mean square error of these rules is less than half that of the sample mean.

B. Efron | C. Morris

[1] F. J. Anscombe,et al. THE TRANSFORMATION OF POISSON, BINOMIAL AND NEGATIVE-BINOMIAL DATA , 1948 .

[2] C. Stein. Inadmissibility of the Usual Estimator for the Mean of a Multivariate Normal Distribution , 1956 .

[3] C. Stein. Confidence Sets for the Mean of a Multivariate Normal Distribution , 1962 .

[4] B. Efron,et al. Studies on toxoplasmosis in El Salvador. Prevalence and incidence of toxoplasmosis as measured by the Sabin-Feldman dye test. , 1970, Transactions of the Royal Society of Tropical Medicine and Hygiene.

[5] B. Efron,et al. Limiting the Risk of Bayes and Empirical Bayes Estimators—Part I: The Bayes Case , 1971 .

[6] B. Efron,et al. Limiting the Risk of Bayes and Empirical Bayes Estimators—Part II: The Empirical Bayes Case , 1972 .

[7] B. Efron,et al. Empirical Bayes on vector observations: An extension of Stein's method , 1972 .

[8] B. Efron,et al. Combining Possibly Related Estimation Problems , 1973 .

[9] B. Efron,et al. Stein's Estimation Rule and Its Competitors- An Empirical Bayes Approach , 1973 .

[10] Grace M. Carter,et al. Empirical Bayes Methods Applied to Estimating Fire Alarm Probabilities , 1974 .

[11] B. Efron. Biased Versus Unbiased Estimation , 1975 .

[12] Bradley Efron,et al. Families of Minimax Estimators of the Mean of a Multivariate Normal Distribution , 1976 .