Slowly decaying correlations, testing normality, nuisance parameters

Beran, Jan; Ghosh, Sucharita

Slowly decaying correlations, testing normality, nuisance parameters

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Date

1991

Authors

Beran, Jan

Ghosh, Sucharita

Publication type

Journal article

Published in

Journal of the American Statistical Association ; 86 (1991), 415. - pp. 785-791

Abstract

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.

Subject (DDC)

510 Mathematics

Keywords

Fractional Gaussian Noise,Goodness-of-fit test,Hermite polynomial,Long-range dependence,Unsuspected correlations

Cite This

ISO 690

BERAN, Jan, Sucharita GHOSH, 1991. Slowly decaying correlations, testing normality, nuisance parameters. In: Journal of the American Statistical Association. 86(415), pp. 785-791. Available under: doi: 10.1080/01621459.1991.10475110

BibTex

@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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