| Title:
|
Some adaptive estimators for slope parameter (English) |
| Author:
|
Viet, Tran Quoc |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
3 |
| Year:
|
1993 |
| Pages:
|
483-500 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
asymptotically optimal score generating function |
| Keyword:
|
Fisher information |
| Keyword:
|
orthonormal system |
| Keyword:
|
rank $(R-)$-estimator |
| Keyword:
|
stopping rule |
| Keyword:
|
asymptotically optimal estimators |
| MSC:
|
62G05 |
| MSC:
|
62G20 |
| MSC:
|
62L12 |
| idZBL:
|
Zbl 0796.62036 |
| idMR:
|
MR1243080 |
| . |
| Date available:
|
2009-01-08T18:05:30Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118605 |
| . |
| Reference:
|
[1] Beran R.: Asymptotically efficient adaptive rank estimates in location models.Ann. Statist. 2 (1974), 63-74. Zbl 0284.62016, MR 0345295 |
| Reference:
|
[2] Billingsley P.: Convergence of Probability Measures.John Wiley, New York, 1968. Zbl 0944.60003, MR 0233396 |
| Reference:
|
[3] Hájek J., Šidák Z.: Theory of Rank tests.Academic Press, Academia, Praha, 1967. MR 0229351 |
| Reference:
|
[4] Hušková M.: Adaptive procedures for the two-sample location model.Commun. Statist. Sequential Analysis 2 (1983-1984), 387-401. MR 0752416 |
| Reference:
|
[5] 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 |
| Reference:
|
[6] Hušková M., Sen P.K.: On sequentially adaptive asymptotically efficient rank statistics.Sequential Analysis 4 (1985), 125-151. MR 0805946 |
| Reference:
|
[7] Rödel E.: Linear rank statistics with estimated scores for testing independence.Statistics, Karl-Weierstraß-Institute of Mathematics, Berlin, 20, pp. 423-438. MR 1012313 |
| Reference:
|
[8] Viet T.Q.: Some adaptive estimators in regression models.Ph.D. Thesis, Charles University, Prague, Czech Republic. |
| Reference:
|
[9] Víšek J.A.: Adaptive estimation in linear regression model.submitted. |
| . |
