Strong consistency of the maximum likelihood estimator for finite mixtures of location-scale distributions when the scale parameters are exponentially small
Strong consistency of the maximum likelihood estimator for finite mixtures of location-scale distributions when the scale parameters are exponentially small
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DOI：
10.3150/bj/1165269148
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发表时间：
2006-12
期刊：
影响因子：
1.5
通讯作者：
Kentaro Tanaka;A. Takemura
中科院分区：
文献类型：
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作者：
Kentaro Tanaka;A. Takemura
在位置-尺度分布的有限混合中，当某些混合分量的尺度参数接近零时，由于似然函数的无界性，最大似然估计量不存在。为了研究极大似然估计的强相合性，我们考虑了分量分布的尺度参数由下而上受c约束的情形。其中{cn}是一个正的真实的数的序列，随着样本大小n的增加，该序列趋于零。证明了在弱正则性条件下，当尺度参数被cn = exp（-nd）9 0限制时，极大似然估计是强相合的
In a finite mixture of location-scale distributions the maximum likelihood estimator does not exist because of the unboundedness of the likelihood function when the scale parameter of some mixture component approaches zero. In order to study the strong consistency of the maximum likelihood estimator, we consider the case where the scale parameters of the component distributions are restricted from below by c?9 where {cn} is a sequence of positive real numbers which tend to zero as the sample size n increases. We prove that under mild regularity conditions the maximum likelihood estimator is strongly consistent if the scale parameters are restricted from below by cn = exp(-nd)9 0