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Stein's method is a general method in probability theory to obtain bounds on the distance between two probability distributions with respect to a probability metric. It was introduced by Charles Stein, who first published it in 1972, to obtain a bound between the distribution of a sum of -dependent sequence of random variables and a standard normal distribution in the Kolmogorov (uniform) metric and hence to prove not only a central limit theorem, but also bounds on the rates of convergence for the given metric. ==History== At the end of the 1960s, unsatisfied with the by-then known proofs of a specific central limit theorem, Charles Stein developed a new way of proving the theorem for his statistics lecture.〔(Charles Stein: The Invariant, the Direct and the "Pretentious" ). Interview given in 2003 in Singapore〕 His seminal paper〔 was presented in 1970 at the sixth Berkeley Symposium and published in the corresponding proceedings. Later, his Ph.D. student Louis Chen Hsiao Yun modified the method so as to obtain approximation results for the Poisson distribution, therefore the Stein method applied to the problem of Poisson approximation is often referred to as the Stein-Chen method. Probably the most important contributions are the monograph by Stein (1986), where he presents his view of the method and the concept of ''auxiliary randomisation'', in particular using ''exchangeable pairs'', and the articles by Barbour (1988) and Götze (1991), who introduced the so-called ''generator interpretation'', which made it possible to easily adapt the method to many other probability distributions. An important contribution was also an article by Bolthausen (1984) on the so-called ''combinatorial central limit theorem''. In the 1990s the method was adapted to a variety of distributions, such as Gaussian processes by Barbour (1990), the binomial distribution by Ehm (1991), Poisson processes by Barbour and Brown (1992), the Gamma distribution by Luk (1994), and many others. 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「Stein's method」の詳細全文を読む スポンサード リンク
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