Some adaptive estimators for slope parameter
Viet, Tran Quoc
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993), p. 483-500 / Harvested from Czech Digital Mathematics Library

An adaptive estimator (of a slope parameter) based on rank statistics is constructed and its asymptotic optimality is studied. A complete orthonormal system is incorporated in the adaptive determination of the score generating function. The proposed sequential procedure is based on a suitable stopping rule. Various properties of the sequential adaptive procedure and the stopping rule are studied. Asymptotic linearity results of linear rank statistics are also studied and some rates of the convergence are established.

Publié le : 1993-01-01
Classification:  62G05,  62G20,  62L12
@article{118605,
     author = {Tran Quoc Viet},
     title = {Some adaptive estimators for slope parameter},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {34},
     year = {1993},
     pages = {483-500},
     zbl = {0796.62036},
     mrnumber = {1243080},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118605}
}
Viet, Tran Quoc. Some adaptive estimators for slope parameter. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 483-500. http://gdmltest.u-ga.fr/item/118605/

Beran R. Asymptotically efficient adaptive rank estimates in location models, Ann. Statist. 2 (1974), 63-74. (1974) | MR 0345295 | Zbl 0284.62016

Billingsley P. Convergence of Probability Measures, John Wiley, New York, 1968. | MR 0233396 | Zbl 0944.60003

Hájek J.; Šidák Z. Theory of Rank tests, Academic Press, Academia, Praha, 1967. | MR 0229351

Hušková M. Adaptive procedures for the two-sample location model, Commun. Statist. Sequential Analysis 2 (1983-1984), 387-401. (1983-1984) | MR 0752416

Hušková M. Sequentially adaptive nonparametric procedures, Handbook of Sequential Analysis, Ghosh B.K. and Sen P.K. (eds.), Reidel, 1991, pp. 459-474. | MR 1174316

Hušková M.; Sen P.K. On sequentially adaptive asymptotically efficient rank statistics, Sequential Analysis 4 (1985), 125-151. (1985) | MR 0805946

Rödel E. Linear rank statistics with estimated scores for testing independence, Statistics, Karl-Weierstraß-Institute of Mathematics, Berlin, 20, pp. 423-438. | MR 1012313

Viet T.Q. Some adaptive estimators in regression models, Ph.D. Thesis, Charles University, Prague, Czech Republic.

Víšek J.A. Adaptive estimation in linear regression model, submitted.