## Tailor-made tests for goodness of fit to semiparametric hypotheses.(English)Zbl 1092.62050

Summary: We introduce a new framework for constructing tests of general semiparametric hypotheses which have nontrivial power on the $$n^{-1/2}$$ scale in every direction, and can be tailored to put substantial power on alternatives of importance. The approach is based on combining test statistics based on stochastic processes of score statistics with bootstrap critical values.

### MSC:

 62G10 Nonparametric hypothesis testing 62G09 Nonparametric statistical resampling methods 62G20 Asymptotic properties of nonparametric inference 62M99 Inference from stochastic processes

### Keywords:

copula models; mixture of Gaussians; independence
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### References:

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