Asymptotic expansion of the risk of maximum likelihood estimator with respect to α-divergence
Asymptotic expansion of the risk of maximum likelihood estimator with respect to α-divergence
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最大似然估计量的风险关于 α 散度的渐近展开
DOI：
10.1080/03610926.2017.1380828
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Yo Sheena
中科院分区：
文献类型：
--
作者：
Masazumi Wakatabe;Toichiro Asada;Asahi Noguchi;Toshiaki Hirai;佐藤公俊;Yo Sheena
对于给定的参数概率模型，我们考虑了极大似然估计关于α散度的风险，它包括Kullback-Leibler散度、Hellinger距离和本质上的χ2散度的特例。给出了风险关于−~2阶样本容量的渐近展开式。展开式中的每一项都用参数概率模型形成的黎曼流形的几何性质来表示。
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 essentially χ2-divergence. The asymptotic expansion of the risk is given with respect to sample sizes up to ordern− 2. Each term in the expansion is expressed with the geometrical properties of the Riemannian manifold formed by the parametric probability model.