Publikation: Slowly decaying correlations, testing normality, nuisance parameters
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Slowly decaying serial correlations can cause goodness-of-fit tests for a distribution to reject the null hypothesis with probability tending to one with increasing sample size. When the null distribution is completely specified (simple null hypothesis) the problem is actually worse than for the case where there are nuisance parameters to be estimated (composite null hypothesis). In particular, we consider here testing normality. We discuss limit theorems and propose correction terms to be incorporated in certain goodness-of-fit statistics to improve the rates of convergence for the simple hypothesis case. We show how the problem is solved automatically for the composite null hypothesis case when the nuisance parameters are estimated from the data. Simulations illustrate the results.
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BERAN, Jan, Sucharita GHOSH, 1991. Slowly decaying correlations, testing normality, nuisance parameters. In: Journal of the American Statistical Association. 1991, 86(415), pp. 785-791. Available under: doi: 10.1080/01621459.1991.10475110BibTex
@article{Beran1991Slowl-18813, year={1991}, doi={10.1080/01621459.1991.10475110}, title={Slowly decaying correlations, testing normality, nuisance parameters}, number={415}, volume={86}, journal={Journal of the American Statistical Association}, pages={785--791}, author={Beran, Jan and Ghosh, Sucharita} }
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