Bootstrap based goodness-of-fit-tests. (English) Zbl 0770.62016
Summary: Let \({\mathcal F}=\{F_ \theta\}\) be a parametric family of distribution functions, and denote with \(F_ n\) the empirical d.f. of an i.i.d. sample. Goodness-of-fit tests of a composite hypothesis (contained in \(\mathcal F\)) are usually based on the so-called estimated empirical process. Typically, they are not distribution-free. In such a situation the bootstrap offers a useful alternative . It is the purpose of this paper to show that this approximation holds with probability one. A simulation study is included which demonstrates the validity of the bootstrap for several selected parametric families.
Keywords:
Kolmogorov-Smirnov distance; Cramer-von Mises distance; logistic distribution; bivariate normal distribution; Weibull distribution; goodness-of-fit tests; composite hypothesis; estimated empirical process; approximation; simulation study; bootstrapReferences:
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