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THE KOMLÓS‐MAJOR‐TUSNÁDY APPROXIMATIONS AND THEIR APPLICATIONS
Author(s) -
CSÖRGÖ SÁNDOR,
Hall Peter
Publication year - 1984
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1984.tb01233.x
Subject(s) - distribution function , sample (material) , invariant (physics) , representation (politics) , mathematics , function (biology) , sequence (biology) , distribution (mathematics) , statistical physics , mathematical analysis , physics , mathematical physics , quantum mechanics , thermodynamics , chemistry , evolutionary biology , biochemistry , politics , biology , political science , law
Summary Any order‐invariant function of a sequence of sample values may be expressed as a functional of the sample's empiric distribution function. This suggests that a very general approach to the theory of functions of sample values can be based on the empiric distribution function. The Komlós‐Major‐Tusnhdy (KMT) approximation provides a remarkable, mathematically tractable representation for the empiric distribution function of a random sample. Our aim in this paper is to describe the KMT approximation, particularly as it relates to other forms of approximation, and to survey some of its many applications.