Second order asymptotic comparison of the MLE and MCLE for a two-sided truncated exponential family of distributions
Second order asymptotic comparison of the MLE and MCLE for a two-sided truncated exponential family of distributions
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双边截断指数分布族的 MLE 和 MCLE 的二阶渐近比较
DOI：
10.1080/03610926.2014.948202
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
K.Koike and N.Ohyauchi
中科院分区：
文献类型：
--
作者：
M.Akahira;S.Hashimoto;K.Koike and N.Ohyauchi
对于具有自然参数θ和截断参数γ作为干扰参数的单侧截断指数族分布，Akahira证明了对于未知γ θ的偏校正极大似然估计量（MLE）相对于对于已知γ θ的极大似然估计量（MLE）的二阶渐近损失，并且最大条件似然估计量（MCLE）是二阶渐近等价的。本文采用与Akahira类似的方法，对具有自然参数θ和两个截断参数γ和ν的双侧截断指数族分布，导出了已知γ和ν的θ的MLE和未知γ和ν的θ的MLE和MCLE的随机展开式，给出了它们的二阶渐近均值和方差，证明了一个经过偏校正的MLE和MLE是二阶渐近等价的。得到了和的二阶渐近损失。进一步给出了包括上截断Pareto情形在内的一些例子。
For a one-sided truncated exponential family of distributions with a natural parameter θ and a truncation parameter γ as a nuisance parameter, it is shown by Akahira that the second-order asymptotic loss of a bias-adjusted maximum likelihood estimator (MLE) of θ for unknown γ relative to the MLE of θ for known γ is given and and the maximum conditional likelihood estimator (MCLE) are second-order asymptotically equivalent. In this paper, in a similar way to Akahira, for a two-sided truncated exponential family of distributions with a natural parameter θ and two truncation parameters γ and ν as nuisance ones, the stochastic expansions of the MLE of θ for known γ and ν and the MLE and the MCLE of θ for unknown γ and ν are derived, their second-order asymptotic means and variances are given, a bias-adjusted MLE and are shown to be second-order asymptotically equivalent, and the second-order asymptotic losses of and relative to are also obtained. Further, some examples including an upper-truncated Pareto case are given.