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august 1999 Regression rank-scores tests against heavy-tailed alternatives
Jana Jureckova
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Bernoulli 5(4): 659-676 (august 1999).


Statistical inference in the linear model based on the concept of regression rank scores is invariant to the nuisance regression; hence regression rank-scores tests need no estimation of the nuisance parameters. Such tests, already available in the literature, are manageable, asymptotically distribution-free and have many convenient properties, but they are either censored or applicable only to light-tailed distributions. To extend the universality of regression rank-scores tests, we propose modified tests applicable to heavy-tailed distributions including Cauchy. Depending on the alternative we want to treat by the test, we censor the score generating function but the censoring is asymptotically negligible. The proposed tests, being asymptotically distribution-free, are as efficient as the ordinary rank tests without nuisance parameters, for a broad class of density shapes.


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Jana Jureckova. "Regression rank-scores tests against heavy-tailed alternatives." Bernoulli 5 (4) 659 - 676, august 1999.


Published: august 1999
First available in Project Euclid: 19 February 2007

zbMATH: 0929.62076
MathSciNet: MR1704560

Keywords: linear regression model , regression quantile , regression rank scores , regression rank test

Rights: Copyright © 1999 Bernoulli Society for Mathematical Statistics and Probability


Vol.5 • No. 4 • august 1999
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