Geodesic
Asymptotic efficiency of inverse estimators
Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 4, pp. 826-844 Cet article a éte moissonné depuis la source Math-Net.Ru

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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: weak convergence, asymptotic efficiency
Mots-clés : inverse estimation, Hájek–LeCam convolution theorem. 
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     title = {Asymptotic efficiency of inverse estimators},
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     language = {en},
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A. C. M. Van Rooij; F. H. Ruymgaart; W. R. Van Zwet. Asymptotic efficiency of inverse estimators. Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 4, pp. 826-844. http://geodesic.mathdoc.fr/item/TVP_1999_44_4_a5/