The Annals of Statistics

Compound decision theory and empirical Bayes methods: invited paper

Cun-Hui Zhang

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Article information

Source
Ann. Statist., Volume 31, Number 2 (2003), 379-390.

Dates
First available in Project Euclid: 22 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aos/1051027872

Digital Object Identifier
doi:10.1214/aos/1051027872

Mathematical Reviews number (MathSciNet)
MR1983534

Subjects
Primary: 62C12: Empirical decision procedures; empirical Bayes procedures 62C25: Compound decision problems
Secondary: 62G08: Nonparametric regression 62G05: Estimation

Keywords
Empirical Bayes compound decision theory nonparametric inference prediction

Citation

Zhang, Cun-Hui. Compound decision theory and empirical Bayes methods: invited paper. Ann. Statist. 31 (2003), no. 2, 379--390. doi:10.1214/aos/1051027872. https://projecteuclid.org/euclid.aos/1051027872


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References

  • BARRON, A., BIRGÉ, L. and MASSART, P. (1999). Risk bounds for model selection via penalization. Probab. Theory Related Fields 113 301-413.
    Mathematical Reviews (MathSciNet): MR2000k:62049
    Zentralblatt MATH: 0946.62036
    Digital Object Identifier: doi:10.1007/s004400050210
  • BENJAMINI, Y. and HOCHBERG, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. J. Roy. Statist. Soc. Ser. B 57 289-300.
    Mathematical Reviews (MathSciNet): MR96d:62143
    JSTOR: links.jstor.org
  • BERGER, J. O. (1980). A robust generalized Bay es estimator and confidence region for a multivariate normal mean. Ann. Statist. 8 716-761.
    Mathematical Reviews (MathSciNet): MR572619
    Zentralblatt MATH: 0464.62026
    Digital Object Identifier: doi:10.1214/aos/1176345068
    Project Euclid: euclid.aos/1176345068
  • BERGER, J. O. (1985). Statistical Decision Theory and Bayesian Analy sis, 2nd ed. Springer, New York.
    Mathematical Reviews (MathSciNet): MR804611
    Zentralblatt MATH: 0572.62008
  • BREIMAN, L., FRIEDMAN, J. H., OLSHEN, R. A. and STONE, C. J. (1984). Classification and Regression Trees. Wadsworth, Belmont, CA.
    Mathematical Reviews (MathSciNet): MR86b:62101
    Zentralblatt MATH: 0541.62042
  • BROWN, L. D. (1966). On the admissibility of invariant estimators of one or more location parameters. Ann. Math. Statist. 37 1087-1136.
    Zentralblatt MATH: 0156.39401
    Mathematical Reviews (MathSciNet): MR216647
    Digital Object Identifier: doi:10.1214/aoms/1177699259
    Project Euclid: euclid.aoms/1177699259
  • CARLIN, B. P. and LOUIS, T. A. (1996). Bay es and Empirical Bay es Methods for Data Analy sis. Chapman and Hall, New York.
    Mathematical Reviews (MathSciNet): MR1427749
  • CARROLL, R. J. and HALL, P. (1988). Optimal rates of convergence for deconvolving a density. J. Amer. Statist. Assoc. 83 1184-1186.
    Zentralblatt MATH: 0673.62033
    Mathematical Reviews (MathSciNet): MR997599
    Digital Object Identifier: doi:10.2307/2290153
    JSTOR: links.jstor.org
  • CARTER, G. and ROLPH, J. (1974). Empirical Bay es methods applied to estimating fire alarm probabilities. J. Amer. Statist. Assoc. 69 880-885.
  • COGBURN, R. (1965). On the estimation of a multivariate location parameter with squared error loss. In Bernoulli, Bay es, and Laplace Anniversary Volume (J. Ney man and L. Le Cam, eds.) 24-29. Springer, Berlin.
    Mathematical Reviews (MathSciNet): MR33:6787
    Zentralblatt MATH: 0147.18404
  • COGBURN, R. (1967). Stringent solutions to statistical decision problems. Ann. Math. Statist. 38 447-463.
    Mathematical Reviews (MathSciNet): MR34:8579
    Zentralblatt MATH: 0155.25203
    Digital Object Identifier: doi:10.1214/aoms/1177698960
    Project Euclid: euclid.aoms/1177698960
  • COPAS, J. B. (1969). Compound decisions and empirical Bay es (with discussion). J. Roy. Statist. Soc. Ser. B 31 397-425.
    Mathematical Reviews (MathSciNet): MR42:3910
    JSTOR: links.jstor.org
  • COPAS, J. B. (1972). Empirical Bay es methods and the repeated use of a standard. Biometrika 59 349-360.
    Mathematical Reviews (MathSciNet): MR49:1655
    Zentralblatt MATH: 0238.62007
    Digital Object Identifier: doi:10.1093/biomet/59.2.349
    JSTOR: links.jstor.org
  • COVER, T. (1968). Learning in pattern recognition. In Methodologies of Pattern Recognition (S. Watanabe, ed.) 111-132. Academic Press, New York.
  • COVER, T. (1991). Universal portfolios. Math. Finance 1 1-29.
    Mathematical Reviews (MathSciNet): MR92c:90023
    Zentralblatt MATH: 0900.90052
    Digital Object Identifier: doi:10.1111/j.1467-9965.1991.tb00002.x
  • DATTA, S. (1991). Asy mptotic optimality of Bay es compound estimators in compact exponential families. Ann. Statist. 19 354-365.
    Mathematical Reviews (MathSciNet): MR92e:62018
    Zentralblatt MATH: 0741.62004
    Digital Object Identifier: doi:10.1214/aos/1176347987
    Project Euclid: euclid.aos/1176347987
  • DEELY, J. J. and KRUSE, R. L. (1968). Construction of sequences estimating the mixing distribution. Ann. Math. Statist. 39 286-288.
    Mathematical Reviews (MathSciNet): MR36:3437
    Zentralblatt MATH: 0174.22302
    Digital Object Identifier: doi:10.1214/aoms/1177698536
    Project Euclid: euclid.aoms/1177698536
  • DEMPSTER, A. P., LAIRD, N. M. and RUBIN, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). J. Roy. Statist. Soc. Ser. B 39 1-38.
    Mathematical Reviews (MathSciNet): MR58:18858
    JSTOR: links.jstor.org
  • DONOHO, D. L. and JOHNSTONE, I. M. (1995). Adapting to unknown smoothness via wavelet shrinkage. J. Amer. Statist. Assoc. 90 1200-1224.
    Mathematical Reviews (MathSciNet): MR96k:62093
    Zentralblatt MATH: 0869.62024
    Digital Object Identifier: doi:10.2307/2291512
    JSTOR: links.jstor.org
  • DONOHO, D. L., JOHNSTONE, I. M., KERKy ACHARIAN, G. and PICARD, D. (1995). Wavelet shrinkage: Asy mptopia? (with discussion). J. Roy. Statist. Soc. Ser. B 57 301-369.
    Mathematical Reviews (MathSciNet): MR96g:62068
    JSTOR: links.jstor.org
  • EFROMOVICH, S. (1999). Nonparametric Curve Estimation. Springer, New York.
    Mathematical Reviews (MathSciNet): MR2000k:62058
  • EFROMOVICH, S. and PINSKER, M. S. (1984). An adaptive algorithm of nonparametric filtering. Autom. Remote Control 11 58-65.
  • EFRON, B. (1996). Empirical Bay es methods for combining likelihoods. J. Amer. Statist. Assoc. 91 538-550.
    Mathematical Reviews (MathSciNet): MR97c:62018
    Zentralblatt MATH: 0868.62018
    Digital Object Identifier: doi:10.2307/2291646
    JSTOR: links.jstor.org
  • EFRON, B. (2003). Robbins, empirical Bay es and microarray s. Ann. Statist. 31 366-378.
    Mathematical Reviews (MathSciNet): MR1983533
    Zentralblatt MATH: 1038.62099
    Digital Object Identifier: doi:10.1214/aos/1051027871
    Project Euclid: euclid.aos/1051027871
  • EFRON, B. and MORRIS, C. (1972a). Empirical Bay es on vector observations: An extension of Stein's method. Biometrika 59 335-347.
    Mathematical Reviews (MathSciNet): MR334386
    Zentralblatt MATH: 0238.62072
    Digital Object Identifier: doi:10.1093/biomet/59.2.335
    JSTOR: links.jstor.org
  • EFRON, B. and MORRIS, C. (1972b). Limiting the risk of Bay es and empirical Bay es estimators. II. The empirical Bay es case. J. Amer. Statist. Assoc. 67 130-139.
    Mathematical Reviews (MathSciNet): MR323015
    Zentralblatt MATH: 0231.62013
    Digital Object Identifier: doi:10.2307/2284711
    JSTOR: links.jstor.org
  • EFRON, B. and MORRIS, C. (1973a). Stein's estimation rule and its competitors-an empirical Bay es approach. J. Amer. Statist. Assoc. 68 117-130.
    Mathematical Reviews (MathSciNet): MR388597
    Zentralblatt MATH: 0275.62005
    Digital Object Identifier: doi:10.2307/2284155
    JSTOR: links.jstor.org
  • EFRON, B. and MORRIS, C. (1973b). Combining possibly related estimation problems (with discussion). J. Roy. Statist. Soc. Ser. B 35 379-421.
    Mathematical Reviews (MathSciNet): MR381112
    JSTOR: links.jstor.org
  • EFRON, B. and MORRIS, C. (1977). Stein's paradox in statistics. Sci. Amer. 236 119-127.
  • EFRON, B., STOREY, J. and TIBSHIRANI, R. (2001). Microarray s, empirical Bay es methods, and false discovery rates. Technical report, Stanford Univ. Available online at http://wwwstat.stanford.edu/ tibs/research.html.
    URL: Link to item
  • EFRON, B., TIBSHIRANI, R., STOREY, J. and TUSHER, V. (2001). Empirical Bay es analysis of a microarray experiment. J. Amer. Statist. Assoc. 96 1151-1160.
    Mathematical Reviews (MathSciNet): MR1946571
    Zentralblatt MATH: 1073.62511
    Digital Object Identifier: doi:10.1198/016214501753382129
    JSTOR: links.jstor.org
  • FAN, J. (1991). On the optimal rates of convergence for nonparametric deconvolution problems. Ann. Statist. 19 1257-1272.
    Zentralblatt MATH: 0729.62033
    Mathematical Reviews (MathSciNet): MR1126324
    Digital Object Identifier: doi:10.1214/aos/1176348248
    Project Euclid: euclid.aos/1176348248
  • FAN, J. and GIJBELS, I. (1996). Local Poly nomial Modeling and Its Applications. Chapman and Hall, London.
    Mathematical Reviews (MathSciNet): MR1383587
    Zentralblatt MATH: 0873.62037
  • FINKELSTEIN, M. O., LEVIN, B. and ROBBINS, H. (1996a). Clinical and prophy lactic trials with assured new treatment for those at greater risk. I. A design proposal. Amer. J. Public Health 86 691-695.
  • FINKELSTEIN, M. O., LEVIN, B. and ROBBINS, H. (1996b). Clinical and prophy lactic trials with assured new treatment for those at greater risk. II. Examples. Amer. J. Public Health 86 696-705.
  • FOX, R. J. (1970). Estimating the empiric distribution function of certain parameter sequences. Ann. Math. Statist. 41 1845-1852.
    Zentralblatt MATH: 0237.62007
    Mathematical Reviews (MathSciNet): MR273737
    Digital Object Identifier: doi:10.1214/aoms/1177696685
    Project Euclid: euclid.aoms/1177696685
  • FRIEDMAN, J. H. (1991). Multivariate adaptive regression splines. Ann. Statist. 19 1-67.
    Zentralblatt MATH: 0765.62064
    Mathematical Reviews (MathSciNet): MR1091842
    Digital Object Identifier: doi:10.1214/aos/1176347963
    Project Euclid: euclid.aos/1176347963
  • GEORGE, E. I. (1986). Minimax multiple shrinkage estimation. Ann. Statist. 14 188-205.
    Mathematical Reviews (MathSciNet): MR87f:62101
    Zentralblatt MATH: 0602.62041
    Digital Object Identifier: doi:10.1214/aos/1176349849
    Project Euclid: euclid.aos/1176349849
  • GEORGE, E. I. and FOSTER, D. P. (2000). Calibration and empirical Bay es variable selection. Biometrika 87 731-747.
    Mathematical Reviews (MathSciNet): MR2001k:62007
    Zentralblatt MATH: 01643823
    Digital Object Identifier: doi:10.1093/biomet/87.4.731
    JSTOR: links.jstor.org
  • GILLILAND, D. C. (1968). Sequential compound estimation. Ann. Math. Statist. 39 1890-1905.
    Mathematical Reviews (MathSciNet): MR44:2291
    Zentralblatt MATH: 0177.46301
    Digital Object Identifier: doi:10.1214/aoms/1177698019
    Project Euclid: euclid.aoms/1177698019
  • GILLILAND, D. C. and HANNAN, J. F. (1969). On an extended compound decision problem. Ann. Math. Statist. 40 1536-1541.
    Mathematical Reviews (MathSciNet): MR41:1160
    Zentralblatt MATH: 0183.47803
    Digital Object Identifier: doi:10.1214/aoms/1177697371
    Project Euclid: euclid.aoms/1177697371
  • GILLILAND, D. C., HANNAN, J. F. and HUANG, J. S. (1976). Asy mptotic solutions to the two state component compound decision problem, Bay es versus diffuse priors on proportions. Ann. Statist. 4 1101-1112.
    Mathematical Reviews (MathSciNet): MR56:6952
    Digital Object Identifier: doi:10.1214/aos/1176343645
    Project Euclid: euclid.aos/1176343645
  • GOOD, I. J. (1953). On the population frequencies of species and the estimation of population parameters. Biometrika 40 237-264.
    Mathematical Reviews (MathSciNet): MR15,809c
    Zentralblatt MATH: 0051.37103
    JSTOR: links.jstor.org
  • HANNAN, J. F. (1957). Approximation to Bay es risk in repeated play. In Contributions to the Theory of Games (M. Dresher and A. W. Tucker, eds.) 3 97-139. Princeton Univ. Press.
  • HANNAN, J. F. and ROBBINS, H. (1955). Asy mptotic solutions of the compound decision problem for two completely specified distributions. Ann. Math. Statist. 26 37-51.
    Mathematical Reviews (MathSciNet): MR16,730e
    Zentralblatt MATH: 0064.38703
    Digital Object Identifier: doi:10.1214/aoms/1177728591
    Project Euclid: euclid.aoms/1177728591
  • HANNAN, J. F. and VAN Ry ZIN, J. R. (1965). Rate of convergence in the compound decision problem for two completely specified distributions. Ann. Math. Statist. 36 1743-1752.
    Mathematical Reviews (MathSciNet): MR32:1813
    Zentralblatt MATH: 0161.37901
    Digital Object Identifier: doi:10.1214/aoms/1177699802
    Project Euclid: euclid.aoms/1177699802
  • HASTIE, T., TIBSHIRANI, R. and FRIEDMAN, J. H. (2001). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, New York.
    Mathematical Reviews (MathSciNet): MR1851606
  • HOADLEY, B. (1981). The quality management plan (QMP). Bell Sy stem Tech. J. 60 215-273.
  • IBRAGIMOV, I. A. and KHASMINSKII, R. Z. (1981). Statistical Estimation: Asy mptotic Theory. Springer, New York.
    Mathematical Reviews (MathSciNet): MR620321
  • JAMES, W. and STEIN, C. (1961). Estimation with quadratic loss. Proc. Fourth Berkeley Sy mp. Math. Statist. Probab. 1 361-379. Univ. California Press, Berkeley.
    Mathematical Reviews (MathSciNet): MR133191
  • JOHNS, M. V. (1957). Non-parametric empirical Bay es procedures. Ann. Math. Statist. 28 649-669.
    Mathematical Reviews (MathSciNet): MR20:2824
    Zentralblatt MATH: 0088.35304
    Digital Object Identifier: doi:10.1214/aoms/1177706877
    Project Euclid: euclid.aoms/1177706877
  • JOHNS, M. V. (1961). An empirical Bay es approach to non-parametric two-way classification. In Studies in Item Analy sis and Prediction (H. Solomon, ed.) 221-232. Stanford Univ. Press.
    Mathematical Reviews (MathSciNet): MR22:12648
    Zentralblatt MATH: 0106.13001
  • JOHNS, M. V. and VAN Ry ZIN, J. R. (1971). Convergence rates for empirical Bay es two-action problems. I. Discrete case. Ann. Math. Statist. 42 1521-1539.
    Mathematical Reviews (MathSciNet): MR303632
    Zentralblatt MATH: 0267.62018
    Digital Object Identifier: doi:10.1214/aoms/1177693151
    Project Euclid: euclid.aoms/1177693151
  • JOHNS, M. V. and VAN Ry ZIN, J. R. (1972). Convergence rates for empirical Bay es two-action problems. II. Continuous case. Ann. Math. Statist. 43 934-947.
    Mathematical Reviews (MathSciNet): MR303633
    Zentralblatt MATH: 0249.62014
    Digital Object Identifier: doi:10.1214/aoms/1177692557
    Project Euclid: euclid.aoms/1177692557
  • KAGAN, A. M. (1962). An empirical Bay es approach to the estimation problem. Dokl. Acad. Sci. U.S.S.R. 147 1020-1021.
    Mathematical Reviews (MathSciNet): MR144413
  • 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.
    Mathematical Reviews (MathSciNet): MR19,189a
    Zentralblatt MATH: 0073.14701
    Digital Object Identifier: doi:10.1214/aoms/1177728066
    Project Euclid: euclid.aoms/1177728066
  • LEVIN, B., ROBBINS, H. and ZHANG, C.-H. (2002). Mathematical aspects of estimating two treatment effects and a common variance in an assured allocation design. J. Statist. Plann. Inference 108 255-262.
    Zentralblatt MATH: 01892381
    Mathematical Reviews (MathSciNet): MR1947402
    Digital Object Identifier: doi:10.1016/S0378-3758(02)00312-9
  • LINDSAY, B. G. (1983). The geometry of mixture likelihoods: A general theory. Ann. Statist. 11 86-94.
    Mathematical Reviews (MathSciNet): MR85m:62008a
    Zentralblatt MATH: 0512.62005
    Digital Object Identifier: doi:10.1214/aos/1176346059
    Project Euclid: euclid.aos/1176346059
  • MARITZ, J. S. and LWIN, T. (1989). Empirical Bay es Methods, 2nd ed. Chapman and Hall, London.
    Mathematical Reviews (MathSciNet): MR1019835
  • MARTZ, H. and KRUTCHKOFF, R. G. (1969). Empirical Bay es estimators in a multiple linear regression model. Biometrika 56 367-374.
  • MEEDEN, G. (1972). Some admissible empirical Bay es procedures. Ann. Math. Statist. 43 96-101.
    Mathematical Reviews (MathSciNet): MR47:9750
    Zentralblatt MATH: 0238.62008
    Digital Object Identifier: doi:10.1214/aoms/1177692705
    Project Euclid: euclid.aoms/1177692705
  • MIy ASAWA, K. (1961). An empirical Bay es estimator of the mean of a normal population. Bull. Internat. Statist. Inst. 38 181-188.
    Mathematical Reviews (MathSciNet): MR27:4303
  • MORRIS, C. N. (1983). Parametric empirical Bay es inference: Theory and applications. J. Amer. Statist. Assoc. 78 47-55.
    Mathematical Reviews (MathSciNet): MR696849
    Zentralblatt MATH: 0506.62005
    Digital Object Identifier: doi:10.2307/2287098
    JSTOR: links.jstor.org
  • NEy MAN, J. (1962). Two breakthroughs in the theory of statistical decision-making. Rev. Internat. Statist. Inst. 30 11-27.
    Mathematical Reviews (MathSciNet): MR28:4646
    Digital Object Identifier: doi:10.2307/1402069
  • OATEN, A. (1972). Approximation to Bay es risk in compound decision problems. Ann. Math. Statist. 43 1164-1184.
    Mathematical Reviews (MathSciNet): MR47:1168
    Zentralblatt MATH: 0241.62005
    Digital Object Identifier: doi:10.1214/aoms/1177692469
    Project Euclid: euclid.aoms/1177692469
  • O'BRy AN, T. E. (1976). Some empirical Bay es results in the case of component problems with varying sample sizes for discrete exponential families. Ann. Statist. 4 1290-1293.
    Mathematical Reviews (MathSciNet): MR56:1526
    Zentralblatt MATH: 0346.62007
    Digital Object Identifier: doi:10.1214/aos/1176343661
    Project Euclid: euclid.aos/1176343661
  • ROBBINS, H. (1951). Asy mptotically subminimax solutions of compound decision problems. Proc. Second Berkeley Sy mp. Math. Statist. Probab. 1 131-148. Univ. California Press, Berkeley.
    Mathematical Reviews (MathSciNet): MR44803
    Zentralblatt MATH: 0044.14803
  • ROBBINS, H. (1956). An empirical Bay es approach to statistics. Proc. Third Berkeley Sy mp. Math. Statist. Probab. 1 157-163. Univ. California Press, Berkeley.
    Mathematical Reviews (MathSciNet): MR18,947e
    Zentralblatt MATH: 0074.35302
  • ROBBINS, H. (1962). Some numerical results on a compound decision problem. In Recent Developments in Information and Decision Processes (R. E. Machol and P. Gray, eds.) 52-62. Macmillan, New York.
  • ROBBINS, H. (1963). The empirical Bay es approach to testing statistical hy potheses. Rev. Internat. Statist. Inst. 31 195-208.
    Mathematical Reviews (MathSciNet): MR32:8448
    Digital Object Identifier: doi:10.2307/1401373
  • ROBBINS, H. (1964). The empirical Bay es approach to statistical decision problems. Ann. Math. Statist. 35 1-20.
    Mathematical Reviews (MathSciNet): MR29:710
    Zentralblatt MATH: 0138.12304
    Digital Object Identifier: doi:10.1214/aoms/1177703729
    Project Euclid: euclid.aoms/1177703729
  • ROBBINS, H. (1968). Estimating the total probability of the unobserved outcomes of an experiment. Ann. Math. Statist. 39 256-257.
    Mathematical Reviews (MathSciNet): MR36:4747
    Zentralblatt MATH: 0155.25801
    Digital Object Identifier: doi:10.1214/aoms/1177698526
    Project Euclid: euclid.aoms/1177698526
  • ROBBINS, H. (1977). Prediction and estimation for the compound Poisson distribution. Proc. Nat. Acad. Sci. U.S.A. 74 2670-2671.
    Mathematical Reviews (MathSciNet): MR56:9761
    Zentralblatt MATH: 0359.62014
    Digital Object Identifier: doi:10.1073/pnas.74.7.2670
    JSTOR: links.jstor.org
  • ROBBINS, H. (1980a). Estimation and prediction for mixtures of the exponential distribution. Proc. Nat. Acad. Sci. U.S.A. 77 2382-2383.
    Mathematical Reviews (MathSciNet): MR570413
    Zentralblatt MATH: 0462.62026
    Digital Object Identifier: doi:10.1073/pnas.77.5.2382
    JSTOR: links.jstor.org
  • ROBBINS, H. (1980b). An empirical Bay es estimation problem. Proc. Nat. Acad. Sci. U.S.A. 77 6988-6989.
    Mathematical Reviews (MathSciNet): MR603064
    Zentralblatt MATH: 0456.62029
    Digital Object Identifier: doi:10.1073/pnas.77.12.6988
    JSTOR: links.jstor.org
  • ROBBINS, H. (1982). Estimating many variances. In Statistical Decision Theory and Related Topics III (S. S. Gupta, ed.) 2 251-261. Academic Press, New York.
    Mathematical Reviews (MathSciNet): MR84j:62011
    Zentralblatt MATH: 0599.62036
  • ROBBINS, H. (1983). Some thoughts on empirical Bay es estimation. Ann. Statist. 11 713-723.
    Mathematical Reviews (MathSciNet): MR85a:62012
    Zentralblatt MATH: 0522.62024
    Digital Object Identifier: doi:10.1214/aos/1176346239
    Project Euclid: euclid.aos/1176346239
  • ROBBINS, H. (1985). Linear empirical Bay es estimation of means and variances. Proc. Nat. Acad. Sci. U.S.A. 82 1571-1574.
    Mathematical Reviews (MathSciNet): MR86f:62017
    Zentralblatt MATH: 0559.62034
    Digital Object Identifier: doi:10.1073/pnas.82.6.1571
    JSTOR: links.jstor.org
  • ROBBINS, H. (1988). The u, v method of estimation. In Statistical Decision Theory and Related Topics IV (S. S. Gupta and J. O. Berger, eds.) 1 265-270. Springer, New York.
    Mathematical Reviews (MathSciNet): MR89a:62070
  • ROBBINS, H. and SAMUEL, E. (1962). Testing statistical hy potheses; the compound approach. In Recent Developments in Information and Decision Processes (R. E. Machol and P. Gray, eds.) 63-70. Macmillan, New York.
  • ROBBINS, H. and ZHANG, C.-H. (1988). Estimating a treatment effect under biased sampling. Proc. Nat. Acad. Sci. U.S.A. 85 3670-3672.
    Mathematical Reviews (MathSciNet): MR89f:62089
    Zentralblatt MATH: 0639.62098
    Digital Object Identifier: doi:10.1073/pnas.85.11.3670
    JSTOR: links.jstor.org
  • ROBBINS, H. and ZHANG, C.-H. (1989). Estimating the superiority of a drug to a placebo when all and only those patients at risk are treated with the drug. Proc. Nat. Acad. Sci. U.S.A. 86 3003-3005.
    Mathematical Reviews (MathSciNet): MR90g:62056
    Zentralblatt MATH: 0665.62108
    Digital Object Identifier: doi:10.1073/pnas.86.9.3003
    JSTOR: links.jstor.org
  • ROBBINS, H. and ZHANG, C.-H. (1991). Estimating a multiplicative treatment effect under biased allocation. Biometrika 78 349-354.
    Mathematical Reviews (MathSciNet): MR92h:62040
    Zentralblatt MATH: 0735.62031
    Digital Object Identifier: doi:10.1093/biomet/78.2.349
    JSTOR: links.jstor.org
  • ROBBINS, H. and ZHANG, C.-H. (2000). Efficiency of the u, v method of estimation. Proc. Nat. Acad. Sci. U.S.A. 97 12976-12979.
    Mathematical Reviews (MathSciNet): MR2001m:62035
    Zentralblatt MATH: 0968.62030
    Digital Object Identifier: doi:10.1073/pnas.97.24.12976
  • RUBIN, D. (1980). Using empirical Bay es techniques in the law school validity studies (with discussion). J. Amer. Statist. Assoc. 75 801-827.
    Mathematical Reviews (MathSciNet): MR590687
    Zentralblatt MATH: 0444.62089
    Digital Object Identifier: doi:10.2307/2287648
  • RUTHERFORD, J. R. and KRUTCHKOFF, R. G. (1967). The empirical Bay es approach: Estimating the prior distribution. Biometrika 54 326-328.
    Mathematical Reviews (MathSciNet): MR35:7463
    Zentralblatt MATH: 0158.17607
    JSTOR: links.jstor.org
  • SAMUEL, E. (1963a). Asy mptotic solutions of the sequential compound decision problem. Ann. Math. Statist. 34 1079-1094.
    Mathematical Reviews (MathSciNet): MR173340
    Zentralblatt MATH: 0202.49102
    Digital Object Identifier: doi:10.1214/aoms/1177704032
    Project Euclid: euclid.aoms/1177704032
  • SAMUEL, E. (1963b). An empirical Bay es approach to the testing of certain parametric hy potheses. Ann. Math. Statist. 34 1370-1385.
    Mathematical Reviews (MathSciNet): MR178554
    Zentralblatt MATH: 0202.49304
    Digital Object Identifier: doi:10.1214/aoms/1177703870
    Project Euclid: euclid.aoms/1177703870
  • SAMUEL, E. (1964). Convergence of the losses of certain decision rules for the sequential compound decision problem. Ann. Math. Statist. 35 1606-1621.
    Mathematical Reviews (MathSciNet): MR31:5302
    Zentralblatt MATH: 0134.35903
    Digital Object Identifier: doi:10.1214/aoms/1177700385
    Project Euclid: euclid.aoms/1177700385
  • SAMUEL, E. (1965). Sequential compound estimators. Ann. Math. Statist. 36 879-889.
    Mathematical Reviews (MathSciNet): MR32:537
    Zentralblatt MATH: 0147.17903
    Digital Object Identifier: doi:10.1214/aoms/1177700060
    Project Euclid: euclid.aoms/1177700060
  • SIMAR, L. (1976). Maximum likelihood estimation of a compound Poisson process. Ann. Statist. 4 1200-1209.
    Mathematical Reviews (MathSciNet): MR55:1603
    Zentralblatt MATH: 0362.62095
    Digital Object Identifier: doi:10.1214/aos/1176343651
    Project Euclid: euclid.aos/1176343651
  • SINGH, R. S. (1979). Empirical Bay es estimation in Lebesgue exponential families with rates near the best possible rate. Ann. Statist. 7 890-902.
    Mathematical Reviews (MathSciNet): MR532252
    Zentralblatt MATH: 0411.62019
    Digital Object Identifier: doi:10.1214/aos/1176344738
    Project Euclid: euclid.aos/1176344738
  • STEIN, C. (1956). Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. Proc. Third Berkeley Sy mp. Math. Statist. Probab. 1 197-206. Univ. California Press, Berkeley.
    Mathematical Reviews (MathSciNet): MR84922
    Zentralblatt MATH: 0073.35602
  • STONE, C. J. (1994). The use of poly nomial splines and their tensor products in multivariate function estimation. Ann. Statist. 22 118-171.
    Mathematical Reviews (MathSciNet): MR1272079
    Zentralblatt MATH: 0827.62038
    Digital Object Identifier: doi:10.1214/aos/1176325361
    Project Euclid: euclid.aos/1176325361
  • STRAWDERMAN, W. E. (1971). Proper Bay es minimax estimators of the multivariate normal mean. Ann. Math. Statist. 42 385-388.
    Mathematical Reviews (MathSciNet): MR53:1794
    Zentralblatt MATH: 0222.62006
    Digital Object Identifier: doi:10.1214/aoms/1177693528
    Project Euclid: euclid.aoms/1177693528
  • SUSARLA, V. (1974). Rate of convergence in the sequence-compound squared-distance loss estimation problem for a family of m-variate normal distributions. Ann. Statist. 2 118- 133.
    Mathematical Reviews (MathSciNet): MR54:6342
    Zentralblatt MATH: 0275.62007
    Digital Object Identifier: doi:10.1214/aos/1176342618
    Project Euclid: euclid.aos/1176342618
  • SUSARLA, V. and VAN Ry ZIN, J. R. (1978). Empirical Bay es estimation of a distribution (survival) function from right-censored observations. Ann. Statist. 6 740-754.
    Mathematical Reviews (MathSciNet): MR81h:62016
    Zentralblatt MATH: 0378.62006
    Digital Object Identifier: doi:10.1214/aos/1176344249
    Project Euclid: euclid.aos/1176344249
  • TEICHER, H. (1961). Identifiability of mixtures. Ann. Math. Statist. 32 244-248.
    Mathematical Reviews (MathSciNet): MR22:11426
    Digital Object Identifier: doi:10.1214/aoms/1177705155
    Project Euclid: euclid.aoms/1177705155
  • TEICHER, H. (1963). Identifiability of finite mixtures. Ann. Math. Statist. 34 1265-1269.
    Mathematical Reviews (MathSciNet): MR27:5310
    Digital Object Identifier: doi:10.1214/aoms/1177703862
    Project Euclid: euclid.aoms/1177703862
  • VAN HOUWELINGEN, H. C. and THOROGOOD, J. (1995). Construction, validation and updating of a prognostic model for kidney graft survival. Statistics in Medicine 14 1999-2008.
  • VAN HOUWELINGEN, J. C. (1977). Monotonizing empirical Bay es estimators for a class of discrete distributions with monotone likelihood ratio. Statist. Neerlandica 31 95-104.
    Mathematical Reviews (MathSciNet): MR57:4388
    Digital Object Identifier: doi:10.1111/j.1467-9574.1977.tb00756.x
  • VAN Ry ZIN, J. R. (1966a). The sequential compound decision problem with m× n finite loss matrix. Ann. Math. Statist. 37 954-975.
  • VAN Ry ZIN, J. R. (1966b). Repetitive play in finite statistical games with unknown distributions. Ann. Math. Statist. 37 976-994.
    Mathematical Reviews (MathSciNet): MR196882
    Zentralblatt MATH: 0173.47802
    Digital Object Identifier: doi:10.1214/aoms/1177699377
    Project Euclid: euclid.aoms/1177699377
  • VAN Ry ZIN, J. R. and SUSARLA, V. (1977). On the empirical Bay es approach to multiple decision problems. Ann. Statist. 5 172-181.
    Mathematical Reviews (MathSciNet): MR55:4455
    Zentralblatt MATH: 0379.62009
    Digital Object Identifier: doi:10.1214/aos/1176343750
    Project Euclid: euclid.aos/1176343750
  • VARDEMAN, S. B. (1978). Admissible solutions of finite state sequence compound decision problems. Ann. Statist. 6 673-679.
    Mathematical Reviews (MathSciNet): MR58:3146
    Zentralblatt MATH: 0388.62010
    Digital Object Identifier: doi:10.1214/aos/1176344211
    Project Euclid: euclid.aos/1176344211
  • WAHBA, G. (1990). Spline Models for Observational Data. SIAM, Philadelphia.
    Mathematical Reviews (MathSciNet): MR91g:62028
    Zentralblatt MATH: 0813.62001
  • WIND, S. L. (1973). An empirical Bay es approach to multiple linear regression. Ann. Statist. 1 93- 103.
    Mathematical Reviews (MathSciNet): MR49:8227
    Zentralblatt MATH: 0253.62007
    Digital Object Identifier: doi:10.1214/aos/1193342385
    Project Euclid: euclid.aos/1193342385
  • ZASLAVSKY, A. M. (1993). Combining census, dual-sy stem, and evaluation study data to estimate population shares. J. Amer. Statist. Assoc. 88 1092-1105.
  • ZHANG, C.-H. (1990). Fourier methods for estimating mixing densities and distributions. Ann. Statist. 18 806-831.
    Zentralblatt MATH: 0778.62037
    Mathematical Reviews (MathSciNet): MR1056338
    Digital Object Identifier: doi:10.1214/aos/1176347627
    Project Euclid: euclid.aos/1176347627
  • ZHANG, C.-H. (1995). On estimating mixing densities in discrete exponential family models. Ann. Statist. 23 929-945.
    Zentralblatt MATH: 0841.62027
    Mathematical Reviews (MathSciNet): MR1345207
    Digital Object Identifier: doi:10.1214/aos/1176324629
    Project Euclid: euclid.aos/1176324629
  • ZHANG, C.-H. (1997). Empirical Bay es and compound estimation of normal means. Statist. Sinica 7 181-193.
    Mathematical Reviews (MathSciNet): MR1441153
    Zentralblatt MATH: 0904.62008
  • ZHANG, C.-H. (2000). General empirical Bay es wavelet methods. Technical Report 2000-007, Dept. Statist., Rutgers Univ., Piscataway, NJ.
  • HILL CENTER, BUSCH CAMPUS
  • PISCATAWAY, NEW JERSEY 08854 E-MAIL: czhang@stat.rutgers.edu

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