论文标题
通过位置尺度有限混合物在Lebesgue空间中的概率密度函数的近似
Approximation of probability density functions via location-scale finite mixtures in Lebesgue spaces
论文作者
论文摘要
从应用和概率和统计的理论角度来看，位置尺度有限混合物类别都引起了人们的持久感兴趣。我们证明了以下结果：以任意程度的准确性，（a）连续概率密度函数（PDF）的位置尺度混合物可以在紧凑的集合上均匀地近似任何连续的PDF； （b）对于任何有限的$ p \ ge1 $，本质上有限的pdf的位置尺度混合物可以在$ \ mathcal {l} _ {p} $中近似任何pdf，in $ \ mathcal {l} _ {p} $。
The class of location-scale finite mixtures is of enduring interest both from applied and theoretical perspectives of probability and statistics. We prove the following results: to an arbitrary degree of accuracy, (a) location-scale mixtures of a continuous probability density function (PDF) can approximate any continuous PDF, uniformly, on a compact set; and (b) for any finite $p\ge1$, location-scale mixtures of an essentially bounded PDF can approximate any PDF in $\mathcal{L}_{p}$, in the $\mathcal{L}_{p}$ norm.
