This article is cited in 1 paper

Recursive estimation of a vector parameter under Bahadur risk

A. P. Korostelev^a, A. L. Rukhin<sup>b

a</sup> Department of Mathematics, Wayne State University, USA
^b Department of Mathematics and Statistics, UMBC, USA

Abstract: Recursive estimation of a vector parameter is investigated when the performance of a procedure is measured by the probability of its closeness to the parameter, i.e., when the loss is defined by a zero-one function. The large deviations of recurrent procedures are studied and asymptotic efficiency of these procedures is explored. The results are extended to the case of a search algorithm in a half-space.

Keywords: Bahadur risk, large deviations, Markov processes, recursive estimation, stochastic approximation.

Received: 01.06.1998

DOI: 10.4213/tvp496

 English version: Theory of Probability and its Applications, 2001, 45:4, 589–603

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