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Empirical Bayes in-season prediction of baseball batting averages

Wenhua Jiang and Cun-Hui Zhang

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Abstract

The performance of a number of empirical Bayes methods are examined for the in-season prediction of batting averages with the 2005 Major League baseball data. Among the methodologies considered are new general empirical Bayes estimators in homoscedastic and heteroscedastic partial linear models.

Chapter information

Source
James O. Berger, T. Tony Cai and Iain M. Johnstone, eds., Borrowing Strength: Theory Powering Applications – A Festschrift for Lawrence D. Brown (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2010), 263-273

Dates
First available in Project Euclid: 26 October 2010

Permanent link to this document
http://projecteuclid.org/euclid.imsc/1288099025

Digital Object Identifier
doi:10.1214/10-IMSCOLL618

Subjects
Primary: 62J05: Linear regression 62J07: Ridge regression; shrinkage estimators
Secondary: 62H12: Estimation 62H25: Factor analysis and principal components; correspondence analysis

Keywords
empirical Bayes compound decisions partial linear model nonparametric estimation semiparametric estimation sports hitting batting average

Rights
Copyright © 2010, Institute of Mathematical Statistics

Citation

Jiang, Wenhua; Zhang, Cun-Hui. Empirical Bayes in-season prediction of baseball batting averages. Borrowing Strength: Theory Powering Applications – A Festschrift for Lawrence D. Brown, 263--273, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2010. doi:10.1214/10-IMSCOLL618. http://projecteuclid.org/euclid.imsc/1288099025.


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References

  • [1] Brown, L. D. (1966). On the admissibility of invariant estimators of one or more location parameters. Ann. Math. Statist. 37 1087–1136.
  • [2] Brown, L. D. (1971). Admissible estimators, recurrent diffusions, and insoluble boundary value problems. Ann. Math. Statist. 42 855–903.
  • [3] Brown, L. D. (2008). In-season prediction of batting averages: A field test of empirical Bayes and Bayes methodologies. Ann. Apply. Statist. 2 113–152.
  • [4] Brown, L. D. and Greenshtein, E. (2009). Empirical Bayes and compound decision approaches for estimation of a high dimensional vector of normal means. Ann. Statist. 37 1685–1704.
  • [5] Brown, L. D. and Zhao, L. H. (2009). Estimators for Gaussian models having a block-wise structure. Statist. Sinica 19 885–903.
  • [6] Donoho, D. L. and Johnstone, I. M. (1994). Minimax risk over p-balls for q-error. Probab. Theory Related Fields 99 277–303.
  • [7] Efron, B. and Morris, C. (1972). Empirical Bayes on vector observations: An extension of Stein’s method. Biometrika 59 335–347.
  • [8] Efron, B. and Morris, C. (1973). Combining possibly related estimation problems (with discussion). J. Roy. Statist. Soc. Ser. B 35 379–421.
  • [9] Greenshtein, E. and Ritov, Y. (2009). Asymptotic efficiency of simple decisions for the compound decision problem. In Optimality: The Third Erich L. Lehmann Symposium (J. Rojo, ed.). IMS Lecture Notes—Monograph Series 57 266–275.
  • [10] James, W. and Stein, C. (1961). Estimation with quadratic loss. In Proc. Fourth Berkeley Symp. Math. Statist. Probab. 1 361–379. Univ. California Press, Berkeley.
  • [11] Jiang, W. and Zhang, C.-H. (2009). General maximum likelihood empirical Bayes estimation of normal means. Ann. Statist. 37 1647–1684.
  • [12] Kiefer, J. and Wolfowitz, J. (1956). Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters. Ann. Math. Statist. 27 887–906.
  • [13] Morris, C. N. (1983). Parametric empirical Bayes inference: Theory and applications. J. Amer. Statist. Assoc. 78 47–55.
  • [14] Robbins, H. (1951). Asymptotically subminimax solutions of compound statistical decision problems. In Proc. Second Berkeley Symp. Math. Statist. Probab. 1 131–148. Univ. California Press, Berkeley.
  • [15] Robbins, H. (1956). An empirical Bayes approach to statistics. In Proc. Third Berkeley Symp. Math. Statist. Probab. 1 157–163. Univ. California Press, Berkeley.
  • [16] Robbins, H. (1983). Some thoughts on empirical Bayes estimation. Ann. Statist. 11 713–723.
  • [17] Stein, C. (1956). Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. In Proc. Third Berkeley Symp. Math. Statist. Probab. 1 157–163. Univ. California Press, Berkeley.
  • [18] Strawderman, W. E. (1971). Proper Bayes estimators of the multivariate normal mean. Ann. Math. Statist. 42 385–388.
  • [19] Strawderman, W. E. (1973). Proper Bayes minimax estimators of the multivariate normal mean for the case of common unknown variances. Ann. Math. Statist. 44 1189–1194.
  • [20] Zhang, C.-H. (1997). Empirical Bayes and compound estimation of normal means. Statist. Sinica 7 181–193.
  • [21] Zhang, C.-H. (2003). Compound decision theory and empirical Bayes method. Ann. Statist. 33 379–390.
  • [22] Zhang, C.-H. (2009). Generalized maximum likelihood estimation of normal mixture densities. Statist. Sinica 19 1297–1318.