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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Horvitz–Thompson estimator ： ウィキペディア英語版 Horvitz–Thompson estimator In statistics, the Horvitz–Thompson estimator, named after Daniel G. Horvitz and Donovan J. Thompson,〔Horvitz, D. G.; Thompson, D. J. (1952) "A generalization of sampling without replacement from a finite universe", ''Journal of the American Statistical Association'', 47, 663–685, . 〕 is a method for estimating the total〔William G. Cochran (1977), ''Sampling Techniques'', 3rd Edition, Wiley. ISBN 0-471-16240-X〕 and mean of a superpopulation in a stratified sample. Inverse probability weighting is applied to account for different proportions of observations within strata in a target population. The Horvitz–Thompson estimator is frequently applied in survey analyses and can be used to account for missing data. ==The method== Formally, let $Y\_i,\; i\; =\; 1,\; 2,\; \backslash ldots,\; n$ be an independent sample from ''n'' of ''N ≥ n'' distinct strata with a common mean ''μ''. Suppose further that $\backslash pi\_i$ is the inclusion probability that a randomly sampled individual in a superpopulation belongs to the ''i''th stratum. The Horvitz–Thompson estimate of the total is given by: : $$ \hat_ = \sum_^n \pi_i ^ Y_i, and the estimate of the mean is given by: : $$ \hat_ = N^\hat_ = N^\sum_^n \pi_i ^ Y_i. In a Bayesian probabilistic framework $\backslash pi\_i$ is considered the proportion of individuals in a target population belonging to the ''i''th stratum. Hence, $\backslash pi\_i^\; Y\_i$ could be thought of as an estimate of the complete sample of persons within the ''i''th stratum. The Horvitz–Thompson estimator can also be expressed as the limit of a weighted bootstrap resampling estimate of the mean. It can also be viewed as a special case of multiple imputation approaches.〔Roderick J.A. Little, Donald B. Rubin (2002) ''Statistical Analysis With Missing Data'', 2nd ed., Wiley. ISBN 0-471-18386-5〕 For post-stratified study designs, estimation of $\backslash pi$ and $\backslash mu$ are done in distinct steps. In such cases, computating the variance of $\backslash hat\_$ is not straightforward. Resampling techniques such as the bootstrap or the jackknife can be applied to gain consistent estimates of the variance of the Horvitz–Thompson estimator. The Survey package for R conducts analyses for post-stratified data using the Horvitz–Thompson estimator. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Horvitz–Thompson estimator」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.