This article is cited in 11 papers

Asymptotic efficiency of inverse estimators

A. C. M. Van Rooij^a, F. H. Ruymgaart^b, W. R. Van Zwet<sup>c

a</sup> Katholieke Universiteit Nijmegen
^b Texas Tech University, Department of Mathematics
^c Rijksuniversiteit Leiden

Abstract: Inverse estimation concerns the recovery of an unknown input signal from blurred observations on a known transformation of that signal. The estimators considered in this paper are based on a regularized inverse of the transformation involved, employing a Hilbert space set-up. We focus on properties related to weak convergence. It is shown that linear functionals can be efficiently estimated in the Hájek–LeCam sense, provided they remain restricted to a suitable class. Outside this class, rates different from $\sqrt{n}$ are possible. By way of an example we present the ‘`convolution theorem’ for a deconvolution.

Keywords: inverse estimation, weak convergence, asymptotic efficiency, Hájek–LeCam convolution theorem.

Received: 12.11.1997
Revised: 28.04.1998

Language: English

DOI: 10.4213/tvp1067

 English version: Theory of Probability and its Applications, 2000, 44:4, 722–738

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