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In theory of probability, the Komlós–Major–Tusnády approximation (also known as the KMT approximation, the KMT embedding, or the Hungarian embedding) is an approximation of the empirical process by a Gaussian process constructed on the same probability space. It is named after Hungarian mathematicians János Komlós, Gábor Tusnády, and Péter Major. ==Theory== Let be independent uniform (0,1) random variables. Define a uniform empirical distribution function as : Define a uniform empirical process as : The Donsker theorem (1952) shows that converges in law to a Brownian bridge Komlós, Major and Tusnády established a sharp bound for the speed of this weak convergence. :Theorem (KMT, 1975) On a suitable probability space for independent uniform (0,1) r.v. the empirical process can be approximated by a sequence of Brownian bridges such that :: :for all positive integers ''n'' and all , where ''a'', ''b'', and ''c'' are positive constants. 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「Komlós–Major–Tusnády approximation」の詳細全文を読む スポンサード リンク
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