小样本下模型选择的最小惩罚Hellinger距离
Minimum penalized Hellinger distance for model selection in small samples
摘要：
在统计建模领域，赤池信息准则AIC是一个广为人知和广泛使用的模型选择工具。散度检验统计量是最近发展起来的一种统计模型选择工具.然而，发散准则的流行度由于其在小样本中缺乏鲁棒性而受到限制。本文研究了惩罚最小Hellinger距离型统计量，并建立了它的一些性质。在原假设和备择假设下，给出了估计和检验统计量的极限律，并推导了幂函数的近似表达式。一个模型选择标准相对于这些分歧措施的参数推断。本文研究的问题是当独立样本从离散总体中抽取时，利用信息型统计量进行模型选择的检验问题。在这里，我们讨论的渐近性质和新的程序测试的性能，并研究其小样本行为。
英文摘要：
In statistical modeling area, the Akaike information criterion AIC, is a widely known and extensively used tool for model choice. The ϕ-divergence test statistic is a recently developed tool for statistical model selection. The popularity of the divergence criterion is however tempered by their known lack of robustness in small sample. In this paper the penalized minimum Hellinger distance type statistics are considered and some properties are established. The limit laws of the estimates and test statistics are given under both the null and the alternative hypotheses, and approximations of the power functions are deduced. A model selection criterion relative to these divergence measures are developed for parametric inference. Our interest is in the problem to testing for choosing between two models using some informational type statistics, when independent sample are drawn from a discrete population. Here, we discuss the asymptotic properties and the performance of new procedure tests and investigate their small sample behavior.
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