asymptotically optimal score generating function; Fisher information; orthonormal system; rank $(R-)$-estimator; stopping rule; asymptotically optimal estimators
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.
 Beran R.: Asymptotically efficient adaptive rank estimates in location models
. Ann. Statist. 2 (1974), 63-74. MR 0345295
| Zbl 0284.62016
 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. 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. 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.