## 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.

### MSC:

 62F05 Asymptotic properties of parametric tests 62F03 Parametric hypothesis testing
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### References:

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