Asymptotic expansion of the risk of maximum likelihood estimator with respect to $α$-divergence as a measure of the difficulty of specifying a parametric model -- with detailed proof

Yo Sheena

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arXiv · 1510.08226

Asymptotic expansion of the risk of maximum likelihood estimator with respect to $α$-divergence as a measure of the difficulty of specifying a parametric model -- with detailed proof

Yo Sheena

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Abstract

For a given parametric probability model, we consider the risk of the maximum likelihood estimator with respect to $α$-divergence, which includes the special cases of Kullback--Leibler divergence, the Hellinger distance and $χ^2$ divergence. The asymptotic expansion of the risk is given with respect to sample sizes of up to order $n^{-2}$. Each term in the expansion is expressed with the geometrical properties of the Riemannian manifold formed by the parametric probability model. We attempt to measure the difficulty of specifying a model through this expansion.

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Yo Sheena. 2018-10-11. Asymptotic expansion of the risk of maximum likelihood estimator with respect to $α$-divergence as a measure of the difficulty of specifying a parametric model -- with detailed proof. https://arxiv.org/abs/1510.08226

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