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Volumn 67, Issue 3, 2005, Pages 343-361

Small confidence sets for the mean of a spherically symmetric distribution

Author keywords

Conditional properties; Confidence sets; Coverage probability; Location parameter; Multivariate normal distribution; Parametric bootstrap; Spherically symmetric distribution; Stein estimator; Volume

Indexed keywords


EID: 20744448988     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2005.00505.x     Document Type: Article
Times cited : (18)

References (41)
  • 1
    • 0000868467 scopus 로고
    • Stein confidence sets and the bootstrap
    • Beran, R. J. (1995) Stein confidence sets and the bootstrap. Statist. Sin., 5, 109-127.
    • (1995) Statist. Sin. , vol.5 , pp. 109-127
    • Beran, R.J.1
  • 2
    • 9844238693 scopus 로고    scopus 로고
    • Diagnosing bootstrap success
    • Beran, R. J. (1997) Diagnosing bootstrap success. Ann. Inst. Statist. Math., 49, 1-24.
    • (1997) Ann. Inst. Statist. Math. , vol.49 , pp. 1-24
    • Beran, R.J.1
  • 3
    • 0011564321 scopus 로고
    • A robust generalized Bayes estimator and confidence region for a multivariate normal mean
    • Berger, J. (1980) A robust generalized Bayes estimator and confidence region for a multivariate normal mean. Ann. Statist., 8, 716-761.
    • (1980) Ann. Statist. , vol.8 , pp. 716-761
    • Berger, J.1
  • 4
    • 20744441786 scopus 로고
    • Spherical distributions
    • Box, G. E. P. (1953) Spherical distributions. Ann. Math. Statist., 24, 687-688.
    • (1953) Ann. Math. Statist. , vol.24 , pp. 687-688
    • Box, G.E.P.1
  • 5
    • 0008708252 scopus 로고
    • Minimax estimation of the mean of spherically symmetric distributions under general quadratic loss
    • Brandwein, A. R. (1979) Minimax estimation of the mean of spherically symmetric distributions under general quadratic loss. J. Multiv. Anal., 9, 579-588.
    • (1979) J. Multiv. Anal. , vol.9 , pp. 579-588
    • Brandwein, A.R.1
  • 6
    • 0012541128 scopus 로고
    • Minimax estimation of location parameters for spherically symmetric unimodal distributions under quadratic loss
    • Brandwein, A. R. and Strawderman, W. E. (1978) Minimax estimation of location parameters for spherically symmetric unimodal distributions under quadratic loss. Ann. Statist., 6, 377-416.
    • (1978) Ann. Statist. , vol.6 , pp. 377-416
    • Brandwein, A.R.1    Strawderman, W.E.2
  • 7
    • 84972526992 scopus 로고
    • Stein estimation: The spherically symmetric case
    • Brandwein, A. and Strawderman, W. (1990) Stein estimation: the spherically symmetric case. Statist. Sci., 5, 356-369.
    • (1990) Statist. Sci. , vol.5 , pp. 356-369
    • Brandwein, A.1    Strawderman, W.2
  • 8
    • 0030335402 scopus 로고    scopus 로고
    • Asymptotic equivalence of nonparametric regression and white noise
    • Brown, L. D. and Low, M. G. (1996) Asymptotic equivalence of nonparametric regression and white noise. Ann. Statist., 24, 2384-2398.
    • (1996) Ann. Statist. , vol.24 , pp. 2384-2398
    • Brown, L.D.1    Low, M.G.2
  • 9
    • 0031322288 scopus 로고    scopus 로고
    • Superefficiency in nonparametric function estimation
    • Brown, L. D., Low, M. G. and Zhao, L. H. (1997) Superefficiency in nonparametric function estimation. Ann. Statist., 25, 2607-2625.
    • (1997) Ann. Statist. , vol.25 , pp. 2607-2625
    • Brown, L.D.1    Low, M.G.2    Zhao, L.H.3
  • 10
    • 20744431989 scopus 로고
    • Some validity criteria for statistical inferences
    • Buehler, R. J. (1959) Some validity criteria for statistical inferences. Ann. Math. Statist., 8, 716-761.
    • (1959) Ann. Math. Statist. , vol.8 , pp. 716-761
    • Buehler, R.J.1
  • 11
    • 0001370552 scopus 로고
    • Empirical Bayes confidence sets for the mean of a multivariate normal distribution
    • Casella, G. and Hwang, J. T. (1983) Empirical Bayes confidence sets for the mean of a multivariate normal distribution. J. Am. Statist. Ass., 78, 688-698.
    • (1983) J. Am. Statist. Ass. , vol.78 , pp. 688-698
    • Casella, G.1    Hwang, J.T.2
  • 13
    • 0041958932 scopus 로고
    • Ideal spatial adaptation by wavelet shrinkage
    • Donoho, D. L. and Johnstone, I. M. (1994) Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81, 425-455.
    • (1994) Biometrika , vol.81 , pp. 425-455
    • Donoho, D.L.1    Johnstone, I.M.2
  • 15
    • 0030519199 scopus 로고    scopus 로고
    • Shrinkage estimators, Skorokhod's problem and stochastic integration by parts
    • Evans, S. and Stark, P. (1996) Shrinkage estimators, Skorokhod's problem and stochastic integration by parts. Ann. Statist., 24, 809-815.
    • (1996) Ann. Statist. , vol.24 , pp. 809-815
    • Evans, S.1    Stark, P.2
  • 16
    • 0039177369 scopus 로고
    • Minimax Bayes set and point estimators of a multivariate normal mean
    • University of Michigan, Ann Arbor
    • Faith, R. E. (1976) Minimax Bayes set and point estimators of a multivariate normal mean. Technical Report 66. University of Michigan, Ann Arbor.
    • (1976) Technical Report , vol.66
    • Faith, R.E.1
  • 19
    • 0347479387 scopus 로고
    • Mathematical probability in the natural sciences
    • Fisher, R. A. (1959) Mathematical probability in the natural sciences, Technometrics, 1, 21-29.
    • (1959) Technometrics , vol.1 , pp. 21-29
    • Fisher, R.A.1
  • 20
    • 0000488448 scopus 로고
    • Minimax confidence sets for the mean of a multivariate normal distribution
    • Hwang, J. T. and Casella, G. (1982) Minimax confidence sets for the mean of a multivariate normal distribution. Ann. Statist., 10, 868-881.
    • (1982) Ann. Statist. , vol.10 , pp. 868-881
    • Hwang, J.T.1    Casella, G.2
  • 21
    • 0001870139 scopus 로고
    • Improved set estimators for a multivariate normal mean
    • Hwang, J. T. and Casella, G. (1984) Improved set estimators for a multivariate normal mean. Statist. Decsns, suppl., 1, 3-16.
    • (1984) Statist. Decsns , vol.1 , Issue.SUPPL. , pp. 3-16
    • Hwang, J.T.1    Casella, G.2
  • 22
    • 0002022550 scopus 로고
    • Improved confidence sets for the coefficients of a linear model with spherically symmetric errors
    • Hwang, J. T. and Chen, J. (1986) Improved confidence sets for the coefficients of a linear model with spherically symmetric errors. Ann. Statist., 14, 444-460.
    • (1986) Ann. Statist. , vol.14 , pp. 444-460
    • Hwang, J.T.1    Chen, J.2
  • 23
    • 0001486499 scopus 로고
    • Estimation with quadratic loss
    • Berkeley: University of California Press
    • James, W. and Stein, C. M. (1961) Estimation with quadratic loss. In Proc. 4th Berkeley Symp. Mathematical Statistics, vol. 1, pp. 361-379. Berkeley: University of California Press.
    • (1961) Proc. 4th Berkeley Symp. Mathematical Statistics , vol.1 , pp. 361-379
    • James, W.1    Stein, C.M.2
  • 24
    • 0011421778 scopus 로고
    • Admissibility of the usual confidence sets for the mean of a univariate or bivariate normal distribution
    • Joshi, V. M. (1969) Admissibility of the usual confidence sets for the mean of a univariate or bivariate normal distribution. Ann. Math. Statist., 38, 1868-1875.
    • (1969) Ann. Math. Statist. , vol.38 , pp. 1868-1875
    • Joshi, V.M.1
  • 25
    • 0001248728 scopus 로고
    • Distribution theory of spherical distributions and a location-scale parameter generalisation
    • Kelker, D. (1970) Distribution theory of spherical distributions and a location-scale parameter generalisation. Sankhya A, 32, 419-430.
    • (1970) Sankhya A , vol.32 , pp. 419-430
    • Kelker, D.1
  • 26
    • 51249177058 scopus 로고
    • Improved confidence set estimators of a multivariate normal mean and generalizations
    • Ki, F. and Tsui, K.-W. (1985) Improved confidence set estimators of a multivariate normal mean and generalizations. Ann. Inst. Statist. Math., 37, 487-498.
    • (1985) Ann. Inst. Statist. Math. , vol.37 , pp. 487-498
    • Ki, F.1    Tsui, K.-W.2
  • 27
    • 38249007618 scopus 로고
    • Estimated confidence procedures for multivariate normal means
    • Lu, K. L. and Berger, J. O. (1989) Estimated confidence procedures for multivariate normal means. J. Statist. Planng Inf., 23, 1-19.
    • (1989) J. Statist. Planng Inf. , vol.23 , pp. 1-19
    • Lu, K.L.1    Berger, J.O.2
  • 28
    • 38249020963 scopus 로고
    • Improved confidence sets for spherically symmetric distributions
    • Robert, C. and Casella, G. (1990) Improved confidence sets for spherically symmetric distributions. J. Multiv. Anal., 32, 84-94.
    • (1990) J. Multiv. Anal. , vol.32 , pp. 84-94
    • Robert, C.1    Casella, G.2
  • 29
    • 0010107098 scopus 로고
    • Improved confidence statements for the usual multivariate normal confidence set
    • New York: Academic Press
    • Robert, C. and Casella, G. (1994) Improved confidence statements for the usual multivariate normal confidence set. In Statistical Decision Theory and Related Topics, vol. V, pp. 351-368. New York: Academic Press.
    • (1994) Statistical Decision Theory and Related Topics , vol.5 , pp. 351-368
    • Robert, C.1    Casella, G.2
  • 30
    • 0000424213 scopus 로고
    • Conditional properties of statistical procedures
    • Robinson, G. K. (1979a) Conditional properties of statistical procedures. Ann. Statist., 7, 742-755.
    • (1979) Ann. Statist. , vol.7 , pp. 742-755
    • Robinson, G.K.1
  • 31
    • 0000424212 scopus 로고
    • Conditional properties of statistical procedures for location and scale parameters
    • Robinson, G. K. (1979b) Conditional properties of statistical procedures for location and scale parameters. Ann. Statist., 1, 756-771.
    • (1979) Ann. Statist. , vol.1 , pp. 756-771
    • Robinson, G.K.1
  • 32
    • 0346295597 scopus 로고    scopus 로고
    • A note on methods of restoring consistency to the bootstrap
    • Samworth, R. J. (2003a) A note on methods of restoring consistency to the bootstrap. Biometrika, 90, 985-990.
    • (2003) Biometrika , vol.90 , pp. 985-990
    • Samworth, R.J.1
  • 34
    • 0039769840 scopus 로고
    • Improved confidence sets for the mean of a multivariate normal distribution
    • Shinozaki, N. (1989) Improved confidence sets for the mean of a multivariate normal distribution. Ann. Inst. Statist. Math., 41, 331-346.
    • (1989) Ann. Inst. Statist. Math. , vol.41 , pp. 331-346
    • Shinozaki, N.1
  • 35
    • 0000813561 scopus 로고
    • Inadmissibility of the usual estimator for the mean of a multivariate normal distribution
    • Berkeley: University of California Press
    • Stein, C. (1956) Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. In Proc. 3rd Berkeley Symp. Mathematical Statistics, vol. 1, pp. 197-206. Berkeley: University of California Press.
    • (1956) Proc. 3rd Berkeley Symp. Mathematical Statistics , vol.1 , pp. 197-206
    • Stein, C.1
  • 36
    • 0011331867 scopus 로고
    • Confidence sets for the mean of a multivariate normal distribution
    • Stein, C. M. (1962) Confidence sets for the mean of a multivariate normal distribution (with discussion). J. R. Statist. Soc. B, 24, 265-296.
    • (1962) J. R. Statist. Soc. B , vol.24 , pp. 265-296
    • Stein, C.M.1
  • 37
    • 0000169918 scopus 로고
    • Estimation of the mean of a multivariate normal distribution
    • Stein, C. (1981) Estimation of the mean of a multivariate normal distribution. Ann. Statist., 9, 1135-1151.
    • (1981) Ann. Statist. , vol.9 , pp. 1135-1151
    • Stein, C.1
  • 39
    • 0031491042 scopus 로고    scopus 로고
    • Good exact confidence sets for a multivariate normal mean
    • Tseng, Y.-L. and Brown, L. D. (1997) Good exact confidence sets for a multivariate normal mean. Ann. Statist., 25, 2228-2258.
    • (1997) Ann. Statist. , vol.25 , pp. 2228-2258
    • Tseng, Y.-L.1    Brown, L.D.2
  • 40
    • 0034393391 scopus 로고    scopus 로고
    • Improved confidence estimators for the multivariate normal confidence set
    • Wang, H. (2000) Improved confidence estimators for the multivariate normal confidence set. Statist. Sin., 10, 659-664.
    • (2000) Statist. Sin. , vol.10 , pp. 659-664
    • Wang, H.1
  • 41
    • 0000723104 scopus 로고
    • Bayesian and non-Bayesian analysis of the regression model with multivariate student-t error terms
    • Zellner, A. (1976) Bayesian and non-Bayesian analysis of the regression model with multivariate student-t error terms. J. Am. Statist. Ass., 71, 400-405.
    • (1976) J. Am. Statist. Ass. , vol.71 , pp. 400-405
    • Zellner, A.1


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