An Essay on Statistical Decision Theory

Journal of the American Statistical Association

Volumn 95, Issue 452, 2000, Pages 1277-1281

  Brown, Lawrence D ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0442309446     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.2000.10474329     Document Type: Article

References (56)

1. Abramowich, F., and Benjamini, Y. (1995), “Threshholding of Wavelet Coefficients as Multiple Testing Procedures,” in Wavelets and Statistics, ed. A. Antoniadis, New York: Springer-Verlag, pp. 5-14.
2. Abramowich, A., Benjamini, Y., Donoho, D., and Johnstone, I. M. (1999), “Sparsity and Threshholding via False Discovery Control,” preprint.
3. 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, Ser. B, 57, 289-300.
4. 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.
5. Bernardo, J. M. (1979), “Reference Prior Distributions for Bayesian Inference,” Journal of the Royal Statistical Society, Ser. B, 41, 113-147.
6. Brown, L. D. (1979), “A Heuristic Method for Determining Admissibility of Estimators, With Applications,” The Annals of Statistics, 7, 960-994.
7. Brown, L. D. (1994), “Minimaxity, More or Less,” in Statistical Decision Theory and Related Topics, eds. S. S. Gupta and J. O. Berger, New York: Springer-Verlag, pp. 1-18.
8. Brown, L. D., Cai, T. T., and DasGupta, A. (1999a), “Interval Estimation for a Binomial Proportion,” submitted for publication.
9. Brown, L. D., Cai, T. T., and DasGupta, A. (1999b), “Confidence Intervals for a Binomial Proportion and Edgeworth Expansions,” submitted for publication.
10. 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.
11. Brown, L. D., and Low, M. G. (1996), “Asymptotic Equivalence of Nonparametric Regression and White Noise,” The Annals of Statistics, 24, 2384-2398.
12. Brown, L. D., Low, M. G., and Zhao, L. H. (1997), “Superefficiency in Nonparametric Function Estimation,” The Annals of Statistics, 25, 2607-2625.
13. Casella, G., and Strawderman, W. E. (1981), “Estimating a Bounded Normal Mean,” The Annals of Statistics, 9, 870-878.
14. 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.
15. Donoho, D. L. (1994), “Statistical Estimation and Optimal Recovery,” The Annals of Statistics, 22, 238-270.
16. Donoho, D. L., and Johnstone, I. M. (1995), “Adapting to Unknown Smoothness via Wavelet Shrinkage,” Journal of the American Statistical Association, 90, 1200-1224.
17. Donoho, D. L., and Johnstone, I. M. (1998), “Minimax Estimation via Wavelet Shrinkage,” The Annals of Statistics, 26, 879-921.
18. Donoho, D. L., and Liu, R. C. (1991), “Geometrizing Rates of Convergence III,” The Annals of Statistics, 19, 668-701.
19. Donoho, D. L., Liu, R. C., and MacGibbon, B. (1990), “Minimax Risk for Hyperrectangles,” The Annals of Statistics, 18, 1416-1437.
20. Eaton, M. L. (1992), “A Statistical Diptych: Admissible Inferences-Recurrence of Symmetric Markov Chains,” The Annals of Statistics, 20, 1147-1179.
21. Efron, B. (1998), “R. A. Fisher in the 21st Century” (with discussion), Statistical Science, 13, 95-113.
22. 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.
23. Hodges, J. L., Jr., and Lehmann, E. L. (1951), “Some Applications of the Cramer-Rao Inequality,” in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1, Berkeley, CA: University of California Press, pp. 13-22.
24. James, W., and Stein, C. (1961), “Estimation With Quadratic Loss,” in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, 1, Berkeley, CA: University of California Press, pp. 311-319.
25. Jennison, C., and Turnbull, B. W. (1990), “Statistical Approaches to Interim Monitoring of Medical Trials: A Review and Commentary,” Statistical Science, 5, 299-317.
26. Johnstone, I. M. (1999), “False Discovery Rates and Adaptive Estimation,” special invited paper presented at the 1999 Joint Statistical Meetings in Baltimore.
27. Kolmogorov, A. (1933), “Sulla Determinazione Empirica di una Leggi di Distribuzione,” Giomale dell’Instituto Italiana degli Attuari, 4, 83-91.
28. Le Cam, L. (1953), On Some Asymptotic Properties of Maximum Likelihood Estimates and Related Bayes Procedures, Berkeley, CA: University of California Press, pp. 277-330.
29. Le Cam, L. (1964), “Sufficiency and Approximate Sufficiency,” Annals of Mathematical Statistics, 35, 1419-1455.
30. Le Cam, L. (1986), Asymptotic Methods in Statistical Decision Theory, New York: Springer-Verlag.
31. Lehmann, E. L., and Casella, G. (1998), Theory of Point Estimation (2nd ed.), New York: Springer.
32. Neyman, J. (1935), “On the Problem of Confidence Intervals,” Annals of Mathematical Statistics, 6, 111-116.
33. Neyman, J. (1941), “Fiducial Argument and the Theory of Confidence Intervals,” Biometrika, 32, 128-150.
34. Neyman, J. (1949), “Contribution to the Theory of the Chi-Square Test,” in Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability, 1945, Berkeley, CA: University of California Press, pp. 239-273.
35. Neyman, J. (1952), Lectures and Conferences on Mathematical Statistics and Probability, Washington, D.C.: U.S. Department of Agriculture.
36. Neyman, J. (1967), A Selection of Early Statistical Papers of J. Neyman, Berkeley, CA: University of California Press.
37. 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.
38. Nussbaum, M. (1996), “Asymptotic Equivalence of Density Estimation and Gaussian White Noise,” The Annals of Statistics, 24, 2399-2430.
39. Parzen, E. (1962), “On the Estimation of a Probability Density and Mode,” Annals of Mathematical Statistics, 33, 1065-1076.
40. Rosenblatt, M. (1956), “Remarks on Some Nonparametric Estimates of a Density Function,” Annals of Mathematical Statistics, 27, 832-837.
41. 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, eds. S. S. Gupta and J. O. Berger, New York: Springer-Verlag, pp. 19-33.
42. 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.
43. Stein, C. (1956a), “Efficient Nonparametric Testing and Estimation,” in Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, CA: University of California Press, pp. 187-196.
44. Stein, C. (1956b), “Inadmissibility of the Usual Estimator for the Mean of a Multivariate Normal Distribution,” in Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, CA: University of California Press, pp. 197-206.
45. Stein, C. (1973), “Estimation of the Mean of a Multivariate Distribution,” in Proceedings of the Prague Symposium on Asymptotic Statistics, pp. 345-381.
46. Stein, C. (1981), “Estimation of the Mean of a Multivariate Normal Distribution,” The Annals of Statistics, 9, 1135-1151.
47. Wald, A. (1939), “Contributions to the Theory of Statistical Estimation and Testing Hypotheses,” Annals of Mathematical Statistics, 10, 299-326.
48. Wald, A. (1942), On the Principles of Statistical Inference, Notre Dame, IN.
49. 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.
50. Wald, A. (1947), Sequential Analysis, New York: Wiley.
51. Wald, A. (1950), Statistical Decision Functions, New York: Wiley.
52. Wald, A., and Wolfowitz, J. (1939), “Confidence Limits for a Continuous Distribution Function,” Annals of Mathematical Statistics, 10, 105-118.
53. Wald, A., and Wolfowitz, J. (1941), “Note on Confidence Limits for Continuous Distribution Functions,” Annals of Mathematical Statistics, 12, 118-119.
54. Wald, A., and Wolfowitz, J. (1950), “Bayes Solution of Sequential Decision Problems,” Annals of Mathematical Statistics, 21, 82-89.
55. Wilson, E. B. (1927), “Probable Inference, the Law of Succession, and Statistical Inference,” Journal of the American Statistical Association, 22, 209-212.
56. Zhao, L. H. (1999), “Improved Estimators in Nonparametric Regression Problems,” Journal of the American Statistical Association, 94, 164-173.