Title: Local Asymptotic Normality of Infinite-Dimensional Concave Extended Linear Models,
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.