文章基本信息

标题：Smoothed Versions of Statistical Functionals from a Finite Population
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作者：Hitoshi Motoyama ; Hajime Takahashi
期刊名称：JOURNAL OF THE JAPAN STATISTICAL SOCIETY
印刷版ISSN：1882-2754
电子版ISSN：1348-6365
出版年度：2008
卷号：38
期号：3
页码：475-504
DOI：10.14490/jjss.38.475
出版社：JAPAN STATISTICAL SOCIETY
摘要：We will consider the central limit theorem for the smoothed version of statistical functionals in a finite population. For the infinite population, Reeds (1976) and Fernholz (1983) discuss the problem under the conditions of Hadamard differentiability of the statistical functionals and derive Taylor type expansions. Lindeberg-Feller's central limit theorem is applied to the leading term, and controlling the remainder terms, the central limit theorem for the statistical functionals are proved. We will modify Fernholz's method and apply it to the finite population with smoothed empirical distribution functions, and we will also obtain Taylor type expansions. We then apply the Erdös-Rényi central limit theorem to the leading linear term to obtain the central limit theorem. We will also obtain sufficient conditions for the central limit theorem, both for the smoothed influence function, and the original non-smoothed versions. Some Monte Carlo simulation results are also included.
关键词：Asymptotic normality;central limit theorem;differentiable functional;empirical distribution function;finite population;functional Taylor series expansions;Hadamard differentiable;influence function;kernel smoothing;official statistics;opinion poll;simple random sampling;statistical functional;survey sampling;uniform topology