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Efficient testing and estimation in two Lehmann alternatives to symmetry-at-zero models

W. J. Hall and Jon A. Wellner

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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.

Chapter information

Source
Banerjee, M., Bunea, F., Huang, J., Koltchinskii, V., and Maathuis, M. H., eds., From Probability to Statistics and Back: High-Dimensional Models and Processes -- A Festschrift in Honor of Jon A. Wellner, (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2013) , 197-212

Dates
First available in Project Euclid: 8 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1362751188

Digital Object Identifier
doi:10.1214/12-IMSCOLL914

Mathematical Reviews number (MathSciNet)
MR3202634

Zentralblatt MATH identifier
1325.62083

Subjects
Primary: 62G07: Density estimation 62H12: Estimation
Secondary: 62G05: Estimation 62G20: Asymptotic properties

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

Rights
Copyright © 2010, Institute of Mathematical Statistics

Citation

Hall, W. J.; Wellner, Jon A. Efficient testing and estimation in two Lehmann alternatives to symmetry-at-zero models. From Probability to Statistics and Back: High-Dimensional Models and Processes -- A Festschrift in Honor of Jon A. Wellner, 197--212, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2013. doi:10.1214/12-IMSCOLL914. https://projecteuclid.org/euclid.imsc/1362751188


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References

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