The role of Hájek's convolution theorem in statistical theory

Beran, Rudolf

Kybernetika, Tome 31 (1995) no. 3, pp. 221-237

Détail

Classification : 62B10, 62F12

Bibliographie

[1] R. R. Bahadur: A note on Fisher's bound for asymptotic variance. Ann. Math. Statist. 55 (1964), 1545-1552. | MR

[2] R. Beran: Estimating a distribution function. Ann. Statist. 5 (1977), 400-404. | MR | Zbl

[3] R. Beran: Estimated sampling distributions: the bootstrap and competitors. Ann. Statist. 10 (1982), 212-225. | MR | Zbl

[4] R. Beran: Bootstrap methods in statistics. Jahresber. Deutsch. Math.-Verein. 86 (1984), 212-225. | MR | Zbl

[5] R. Beran: Confidencesets centered at Cp-estimators. Unpublished preprint (1994).

[6] P. J. Bickel, D. F. Freedman: Some asymptotic theory for the bootstrap. Ann. Statist. 9 (1981), 1196-1217. | MR | Zbl

[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

[8] J. Bretagnolle: Lois limites du bootstrap de certaines fonctionnelles. Ann. Inst. Henri Poincare X9 (1983), 281-296. | MR | Zbl

[9] G. Casella, T. J. Hwang: Limit expressions for the risk of James-Stein estimators. Canad. J. Statist. 10 (1982), 305-309. | MR | Zbl

[10] H. Chernoff: Large sample theory: parametric case. Ann. Math. Statist. 21 (1956), 1-22. | MR | Zbl

[11] H. Cramer: A contribution to the theory of statistical estimation. Skand. Akt. Tidskr. 29 (1946), 85-94. | MR | Zbl

[12] G. Darmois: Sur les lois limites de la dispersion de certaines estimations. Rev. Inst. Internat. Statist. 13 (1945), 9-15.

[13] W. Droste, W. Wefelmeyer: On Hajek's convolution theorem. Statist. Decisions 2 (1984), 131-144. | MR | Zbl

[14] B. Efron: Bootstrap methods: Another look at the jackknife. Ann. Statist. 7 (1979), 1-26 | MR | Zbl

[15] R. A. Fisher: Theory of statistical estimation. Proc. Cambridge Philos. Soc. 22(1925), 700-725.

[16] M. Frechet: Sur l'extension de certaines evaluations statistiques de petit echantillons. Rev. Inst. Internat. Statist. 11 (1943), 182-205.

[17] J. Hájek: A characterization of limiting distributions of regular estimates. Z. Wahrsch. verw. Gebiete 14 (1970), 323-330. | MR

[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

[19] J. Hájek, Z. Šidák: Theory of Rank Tests. Academic Press, New York 1967. | MR

[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. | MR | Zbl

[21] I. A. Ibragimov, R. Z. Hasminskii: Statistical Estimation: Asymptotic Theory. Springer, New York 1981. | MR

[22] N. Inagaki: On the limiting distribution of a sequence of estimators with uniformity property. Ann. Inst. Statist. Math. 22 (1970), 1-13. | MR | Zbl

[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

[24] P. Jeganathan: On a decomposition of the limit distribution of a sequence- of estimators. Sankhya (Ser. A) 43 (1981), part 1, 26-36. | MR | Zbl

[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. | MR | Zbl

[26] S. Kaufman: Asymptotic efficiency of the maximum likelihood estimator. Ann. Inst. Statist. Math. 18 (1966), 155-178. | MR | Zbl

[27] Yu. A. Koshevnik, B. Ya. Levit: On a nonparametric analog of the information matrix. Theory Probab. Appl. 21 (1975), 738-753.

[28] L. LeCam: On some asymptotic properties of maximum likelihood estimates and related Bayes estimates. Univ. California Publ. Statist. 1 (1953), 277-330. | MR

[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

[30] L. LeCam: Locally asymptotically normal families of distributions. Univ. California Publ. Statist. 3 (1960), 27-98. | MR

[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

[32] L. LeCam: Sur les contraintes imposees par les passages a limite usuels en statististique. Bull. Inst. Internat. Statist. 45 (1972), 169-180. | MR

[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

[34] L. LeCam: Asymptotic Methods in Statistical Decision Theory. Springer, New York 1986. | MR

[35] L. LeCam, G. L. Yang: Asymptotics in Statistics. Springer, New York 1990. | MR

[36] E. L. Lehmann: Theory of Point Estimation. Wiley, New York 1983. | MR | Zbl

[37] B. Ya. Levit: On the efficiency of a class of nonparametric estimates. Theory Probab. Appl. 20 (1975), 723-740.

[38] P. W. Millar: Non-parametric applications of an infinite dimensional convolution theorem. Z. Wahrsch. verw. Gebiete 68 (1985), 545-556. | MR | Zbl

[39] J. Pfanzagl: Parametric Statistical Theory. Walter de Gruyter, Berlin 1994. | MR | Zbl

[40] J. Pfanzagl, W. Wefelmeyer: Contributions to a General Asymptotic Statistical Theory. (Lecture Notes in Statistics 13.) Springer, New York 1982. | MR | Zbl

[41] M. S. Pinsker: Optimal filtration of square-integrable signals in Gaussian white noise. Problems Inform. Transmission 16 (1980), 120-133. | MR

[42] B. Potscher: Comment on "The effect of model selection on confidence regions and prediction regions" by P. Kabaila. Econometric Theory, to appear. | MR

[43] J. W. Pratt: F. Y. Edgeworth, R. A. Fisher: On the efficiency of maximum likelihood estimation. Ann. Statist. 4 (1976), 501-514. | MR

[44] C. R. Rao: Information and accuracy attainable in the estimation of statistical parameters. Bull. Calcutta Math. Soc. 57 (1945), 81-91. | MR

[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. | MR | Zbl

[46] G. R. Roussas: Contiguous Probability Measures: Some Applications in Statistics. Cambridge Univ. Press, Cambridge 1972.

[47] L. J. Savage: On rereading R. A. Fisher. Ann. Statist. 4 (1976), 441-500. | MR | Zbl

[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

[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. | MR | Zbl

[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. | MR | Zbl

[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

[52] A. van der Vaart: Statistical Estimation in Large Parameter Spaces. CWI Tracts 44, Centrum voor Wiskunde en Informatica, Amsterdam 1988. | MR | Zbl

[53] A. van der Vaart: On the asymptotic information bound. Ann. Statist 17 (1989), 1487-1500. | MR | Zbl

[54] J. Wolfowitz: Asymptotic efficiency of the maximum likelihood estimator. Theory Probab. Appl. 10 (1965), 247-260. | MR | Zbl