| Title:
|
The role of Hájek's convolution theorem in statistical theory (English) |
| Author:
|
Beran, Rudolf |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
31 |
| Issue:
|
3 |
| Year:
|
1995 |
| Pages:
|
221-237 |
| . |
| Category:
|
math |
| . |
| MSC:
|
62B10 |
| MSC:
|
62F12 |
| idZBL:
|
Zbl 0848.62014 |
| idMR:
|
MR1337978 |
| . |
| Date available:
|
2009-09-24T18:55:08Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/124721 |
| . |
| Reference:
|
[1] R. R. Bahadur: A note on Fisher's bound for asymptotic variance.Ann. Math. Statist. 55 (1964), 1545-1552. MR 0166867 |
| Reference:
|
[2] R. Beran: Estimating a distribution function.Ann. Statist. 5 (1977), 400-404. Zbl 0379.62024, MR 0445701 |
| Reference:
|
[3] R. Beran: Estimated sampling distributions: the bootstrap and competitors.Ann. Statist. 10 (1982), 212-225. Zbl 0485.62037, MR 0642733 |
| Reference:
|
[4] R. Beran: Bootstrap methods in statistics.Jahresber. Deutsch. Math.-Verein. 86 (1984), 212-225. Zbl 0547.62023, MR 0736625 |
| Reference:
|
[5] R. Beran: Confidencesets centered at Cp-estimators.Unpublished preprint (1994). |
| Reference:
|
[6] P. J. Bickel, D. F. Freedman: Some asymptotic theory for the bootstrap.Ann. Statist. 9 (1981), 1196-1217. Zbl 0449.62034, MR 0630103 |
| Reference:
|
[7] P. J. Bickel C. A. Klaassen Y. Ritov, J. A. Wellner: Efficient and Adaptive Estimation for Semiparametric Models.Johns Hopkins Univ. Press, Baltimore 1993. MR 1245941 |
| Reference:
|
[8] J. Bretagnolle: Lois limites du bootstrap de certaines fonctionnelles.Ann. Inst. Henri Poincare X9 (1983), 281-296. Zbl 0535.62046, MR 0725561 |
| Reference:
|
[9] G. Casella, T. J. Hwang: Limit expressions for the risk of James-Stein estimators.Canad. J. Statist. 10 (1982), 305-309. Zbl 0512.62044, MR 0701585 |
| Reference:
|
[10] H. Chernoff: Large sample theory: parametric case.Ann. Math. Statist. 21 (1956), 1-22. Zbl 0072.35703, MR 0076245 |
| Reference:
|
[11] H. Cramer: A contribution to the theory of statistical estimation.Skand. Akt. Tidskr. 29 (1946), 85-94. Zbl 0060.30513, MR 0017505 |
| Reference:
|
[12] G. Darmois: Sur les lois limites de la dispersion de certaines estimations.Rev. Inst. Internat. Statist. 13 (1945), 9-15. |
| Reference:
|
[13] W. Droste, W. Wefelmeyer: On Hajek's convolution theorem.Statist. Decisions 2 (1984), 131-144. Zbl 0536.62020, MR 0746129 |
| Reference:
|
[14] B. Efron: Bootstrap methods: Another look at the jackknife.Ann. Statist. 7 (1979), 1-26 Zbl 0406.62024, MR 0515681 |
| Reference:
|
[15] R. A. Fisher: Theory of statistical estimation.Proc. Cambridge Philos. Soc. 22(1925), 700-725. |
| Reference:
|
[16] M. Frechet: Sur l'extension de certaines evaluations statistiques de petit echantillons.Rev. Inst. Internat. Statist. 11 (1943), 182-205. |
| Reference:
|
[17] J. Hájek: A characterization of limiting distributions of regular estimates.Z. Wahrsch. verw. Gebiete 14 (1970), 323-330. MR 0283911 |
| Reference:
|
[18] J. Hájek: Local asymptotic minimax and admissibility in estimation.In: Proc. Sixth Berkeley Symp. Math. Statist. Prob. (L. M. LeCam, J. Neyman and E. M. Scott, eds.), 1, Univ. California Press, Berkeley 1972, pp. 175-194. MR 0400513 |
| Reference:
|
[19] J. Hájek, Z. Šidák: Theory of Rank Tests.Academic Press, New York 1967. MR 0229351 |
| Reference:
|
[20] B. M. Hill: The three-parameter lognormal distribution and Bayesian analysis of a point source epidemic.J. Amer. Statist. Assoc. 58 (1963), 72-84. Zbl 0121.13905, MR 0144407 |
| Reference:
|
[21] I. A. Ibragimov, R. Z. Hasminskii: Statistical Estimation: Asymptotic Theory.Springer, New York 1981. MR 0620321 |
| Reference:
|
[22] N. Inagaki: On the limiting distribution of a sequence of estimators with uniformity property.Ann. Inst. Statist. Math. 22 (1970), 1-13. Zbl 0282.62028, MR 0273725 |
| Reference:
|
[23] W. James, C. Stein: Estimation with quadratic loss.In: Proc. Fourth Berkeley Symp. Math. Statist. Prob. (J. Neyman, ed.) 1, Univ. California Press, Berkeley 1961, pp. 361-380. MR 0133191 |
| Reference:
|
[24] P. Jeganathan: On a decomposition of the limit distribution of a sequence- of estimators.Sankhya (Ser. A) 43 (1981), part 1, 26-36. Zbl 0512.62043, MR 0656266 |
| Reference:
|
[25] P. Jeganathan: On the asymptotic theory of estimation when the limit of the log-likelihood ratios is mixed normal.Sankhya (Ser. A) 44 (1982), part 2, 173-212. Zbl 0584.62042, MR 0688800 |
| Reference:
|
[26] S. Kaufman: Asymptotic efficiency of the maximum likelihood estimator.Ann. Inst. Statist. Math. 18 (1966), 155-178. Zbl 0144.41302, MR 0211521 |
| Reference:
|
[27] Yu. A. Koshevnik, B. Ya. Levit: On a nonparametric analog of the information matrix.Theory Probab. Appl. 21 (1975), 738-753. |
| Reference:
|
[28] L. LeCam: On some asymptotic properties of maximum likelihood estimates and related Bayes estimates.Univ. California Publ. Statist. 1 (1953), 277-330. MR 0054913 |
| Reference:
|
[29] L. LeCam: On the asymptotic theory of estimation and testing hypotheses.In: Proc. Third Berkeley Symp. Math. Statist. Prob. (J. Neyman, ed.) 1, Univ. California Press, Berkeley 1956, pp. 129-156. MR 0084918 |
| Reference:
|
[30] L. LeCam: Locally asymptotically normal families of distributions.Univ. California Publ. Statist. 3 (1960), 27-98. MR 0126903 |
| Reference:
|
[31] L. LeCam: Limits of experiments.In: Proc. Sixth Berkeley Symp. Math. Statist. Prob. (L.M. LeCam, J. Neyman, and E. M. Scott, eds.), 1, Univ. California Press, Berkeley 1972, pp. 245-261. MR 0415819 |
| Reference:
|
[32] L. LeCam: Sur les contraintes imposees par les passages a limite usuels en statististique.Bull. Inst. Internat. Statist. 45 (1972), 169-180. MR 0373104 |
| Reference:
|
[33] L. LeCam: On a theorem of J. Hájek.In: Contributions to Statistics: J. Hájek Memorial Volume (J. Jurečková, ed.), Academia, Prague 1979, pp. 119-137. MR 0561265 |
| Reference:
|
[34] L. LeCam: Asymptotic Methods in Statistical Decision Theory.Springer, New York 1986. MR 0856411 |
| Reference:
|
[35] L. LeCam, G. L. Yang: Asymptotics in Statistics.Springer, New York 1990. MR 1066869 |
| Reference:
|
[36] E. L. Lehmann: Theory of Point Estimation.Wiley, New York 1983. Zbl 0522.62020, MR 0702834 |
| Reference:
|
[37] B. Ya. Levit: On the efficiency of a class of nonparametric estimates.Theory Probab. Appl. 20 (1975), 723-740. |
| Reference:
|
[38] P. W. Millar: Non-parametric applications of an infinite dimensional convolution theorem.Z. Wahrsch. verw. Gebiete 68 (1985), 545-556. Zbl 0571.62031, MR 0772198 |
| Reference:
|
[39] J. Pfanzagl: Parametric Statistical Theory.Walter de Gruyter, Berlin 1994. Zbl 0807.62016, MR 1291393 |
| Reference:
|
[40] J. Pfanzagl, W. Wefelmeyer: Contributions to a General Asymptotic Statistical Theory.(Lecture Notes in Statistics 13.) Springer, New York 1982. Zbl 0512.62001, MR 0675954 |
| Reference:
|
[41] M. S. Pinsker: Optimal filtration of square-integrable signals in Gaussian white noise.Problems Inform. Transmission 16 (1980), 120-133. MR 0624591 |
| Reference:
|
[42] B. Potscher: Comment on "The effect of model selection on confidence regions and prediction regions" by P. Kabaila.Econometric Theory, to appear. MR 1349934 |
| Reference:
|
[43] J. W. Pratt: F. Y. Edgeworth, R. A. Fisher: On the efficiency of maximum likelihood estimation.Ann. Statist. 4 (1976), 501-514. MR 0415867 |
| Reference:
|
[44] C. R. Rao: Information and accuracy attainable in the estimation of statistical parameters.Bull. Calcutta Math. Soc. 57 (1945), 81-91. MR 0015748 |
| Reference:
|
[45] G. G. Roussas: Some applications of the asymptotic distribution of likelihood functions to the asymptotic efficiency of estimates.Z. Wahrsch. verw. Gebiete 10 (1968), 252-260. Zbl 0167.17705, MR 0242300 |
| Reference:
|
[46] G. R. Roussas: Contiguous Probability Measures: Some Applications in Statistics.Cambridge Univ. Press, Cambridge 1972. |
| Reference:
|
[47] L. J. Savage: On rereading R. A. Fisher.Ann. Statist. 4 (1976), 441-500. Zbl 0325.62008, MR 0403889 |
| Reference:
|
[48] L. Schmetterer: On asymptotic efficiency of estimates.In: Research Papers in Statistics: Festschrift for J. Neyman (F. N. David, ed.), Wiley, New York 1966, pp. 310-317. MR 0210231 |
| Reference:
|
[49] C. Stein: Efficient nonparametric testing and estimation.In: Proc. Third Berkeley Symp. Math. Statist. Prob. (J. Neyman, ed.), 1, Univ. California Press, Berkeley 1956, pp. 187-195. Zbl 0074.34801, MR 0084921 |
| Reference:
|
[50] C. Stein: Inadmissibility of the usual estimator for the mean of a multivariate normal distribution.In: Proc. Third Berkeley Symp. Math. Statist. Prob. (J. Neyman, ed.), 1, Univ. California Press, Berkeley 1956, pp. 197-206. Zbl 0073.35602, MR 0084922 |
| Reference:
|
[51] D. M. Titterington: Choosing the regularization parameter in image restoration.In: Spatial Statistics and Imaging (A. Possolo, ed.), IMS Lecture Notes - Monograph Series 20 (1991), 392-402. MR 1195573 |
| Reference:
|
[52] A. van der Vaart: Statistical Estimation in Large Parameter Spaces.CWI Tracts 44, Centrum voor Wiskunde en Informatica, Amsterdam 1988. Zbl 0629.62035, MR 0927725 |
| Reference:
|
[53] A. van der Vaart: On the asymptotic information bound.Ann. Statist 17 (1989), 1487-1500. Zbl 0698.62033, MR 1026295 |
| Reference:
|
[54] J. Wolfowitz: Asymptotic efficiency of the maximum likelihood estimator.Theory Probab. Appl. 10 (1965), 247-260. Zbl 0142.15402, MR 0184338 |
| . |
