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Estimating the distribution function of symmetric pairs

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  • Reza Modarres

Abstract

We discuss three classes of bivariate symmetry models and study the estimation of their distribution functions (DFs). Under radial symmetry, an estimator based on the mean of the empirical and survival DFs is considered. For exchangeable symmetry, an estimator based on the mean of the empirical DF and its exchangeable image is presented. At their intersection, we define radial exchangeability and study estimation of its DF. The symmetrized estimators coincide with the non parametric maximum likelihood estimators of the DF under each model. We obtain their mean and variance and state their asymptotic normality. The relative efficiency of the estimators for the bivariate normal distribution is obtained.

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  • Reza Modarres, 2017. "Estimating the distribution function of symmetric pairs," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(4), pages 1843-1854, February.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:4:p:1843-1854
    DOI: 10.1080/03610926.2015.1030421
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