文章基本信息

标题：Parametric Stein operators and variance bounds
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作者：Christophe Ley ; Yvik Swan
期刊名称：Brazilian Journal of Probability and Statistics
印刷版ISSN：0103-0752
出版年度：2016
卷号：30
期号：2
页码：171-195
DOI：10.1214/14-BJPS271
语种：English
出版社：Brazilian Statistical Association
摘要：Stein operators are (differential/difference) operators which arise within the so-called Stein’s method for stochastic approximation. We propose a new mechanism for constructing such operators for arbitrary (continuous or discrete) parametric distributions with continuous dependence on the parameter. We provide explicit general expressions for location, scale and skewness families. We also provide a general expression for discrete distributions. We use properties of our operators to provide upper and lower variance bounds (only lower bounds in the discrete case) on functionals $h(X)$ of random variables $X$ following parametric distributions. These bounds are expressed in terms of the first two moments of the derivatives (or differences) of $h$. We provide general variance bounds for location, scale and skewness families and apply our bounds to specific examples (namely the Gaussian, exponential, gamma and Poisson distributions). The results obtained via our techniques are systematically competitive with, and sometimes improve on, the best bounds available in the literature.