Translator Disclaimer
VOL. 9 | 2013 Efficient testing and estimation in two Lehmann alternatives to symmetry-at-zero models
W. J. Hall, Jon A. Wellner

Editor(s) M. Banerjee, F. Bunea, J. Huang, V. Koltchinskii, M. H. Maathuis

## Abstract

We consider two variations on a Lehmann alternatives to symmetry-at-zero semiparametric model, with a real parameter $\theta$ quantifying skewness and a symmetric-at-0 distribution as a nuisance function. We show that a test of symmetry based on the signed log-rank statistic [A signed log-rank test of symmetry at zero (2011) University of Rochester] is asymptotically efficient in these models, derive its properties under local alternatives and present efficiency results relative to other signed-rank tests. We develop efficient estimation of the primary parameter in each model, using model-specific estimates of the nuisance function, and provide a method for choosing between the two models. All inference methods proposed are based solely on the signed ranks of the absolute values of the observations, the invariantly sufficient statistic. A simulation study is summarized and an example presented. Extensions to regression modeling are envisaged.

## Information

Published: 1 January 2013
First available in Project Euclid: 8 March 2013

zbMATH: 1325.62083
MathSciNet: MR3202634

Digital Object Identifier: 10.1214/12-IMSCOLL914

Subjects:
Primary: 62G07 , 62H12
Secondary: 62G05 , 62G20

Keywords: asymptotically uniformly most powerful test , information bound , proportional hazards , reversed hazards , semiparametric models , signed log-rank test