Local Asymptotic Normality of Infinite-Dimensional Concave Extended Linear Models

Kosaku Takanashi
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Kosaku Takanashi: Faculty of Economics, Keio University

No 2017-012, Keio-IES Discussion Paper Series from Institute for Economics Studies, Keio University

Abstract: We study local asymptotic normality of M-estimates of convex minimization in an infinite dimensional parameter space. The objective function of M-estimates is not necessary differentiable and is possibly subject to convex constraints. In the above circumstance, narrow convergence with respect to uniform convergence fails to hold, because of the strength of it's topology. A new approach we propose to the lack-of-uniform-convergence is based on Mosco-convergence that is weaker topology than uniform convergence. By applying narrow convergence with respect to Mosco topology, we develop an infinite-dimensional version of the convexity argument and provide a proof of a local asymptotic normality. Our new technique also provides a proof of an asymptotic distribution of the likelihood ratio test statistic defined on real separable Hilbert spaces.

Keywords: Epi-convergence; Likelihood ratio test; Local asymptotic normality; Mosco-topology (search for similar items in EconPapers)
JEL-codes: C12 C14 (search for similar items in EconPapers)
Pages: 28 pages
Date: 2017-04-10
New Economics Papers: this item is included in nep-ecm
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