Title: The Probability Integral Transformation for Non Necessarily Absolutely Continuous Distribution Functions, and its Application to Goodness-of-Fit Tests
Abstract: To any probability measure Q on ℝk, it is possible to associate a probability transition (i.e. a Markov kernel) QR, from ℝk to [0,1]k, such that the composition of Q by QR is the uniform probability (or Lebesgue measure) on [0,1]k; QR is called the probability integral transform (p.i.t) of Q. P being a class of probability measures on a space of observations Z, let φ be a P sufficient mapping from Z to a space Y, and ξ a mapping from Z to ℝk; let, for every z, ψ(z) be the probability associated to point ξ(z) (in ℝk) by the p.i.t of the law of ξ for any probability measure deduced from P (in P) through conditioning by [φ = φ(z)]; for any P in P, the composition of P by ψ is the uniform probability on [0,1]k; this property gives a general method of construction of goodness-of-fit tests for P; properties of these tests are discussed, with respect to the choice of the mappings φ and ξ.
Publication Year: 1983
Publication Date: 1983-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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