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Estimation of a bivariate symmetric distribution function

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  • Modarres, Reza

Abstract

We consider the efficient estimation of a bivariate distribution function (DF) under the class of radially symmetric distributions and propose an estimator based on the mean of the empirical distribution and survival functions. We obtain the mean and variance of the estimator and show that it has an asymptotic normal distribution. We also show that the nonparametric maximum likelihood estimator of the bivariate DF coincides with the new estimator under radial symmetry. We study the asymptotic relative efficiency of this estimator and show that it results in a minimum of 50% reduction in sample size over the empirical DF at any point (x,y) in . A bootstrap procedure to test whether the data support a radially symmetric model is examined. A simulation study compares the size and power of this test under bivariate normality, against alternatives in the Plackett's family of bivariate distributions, to two other procedures based on Kolmogorov-Smirnov distance.

Suggested Citation

  • Modarres, Reza, 2003. "Estimation of a bivariate symmetric distribution function," Statistics & Probability Letters, Elsevier, vol. 63(1), pages 25-34, May.
    • Handle: RePEc:eee:stapro:v:63:y:2003:i:1:p:25-34
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    References listed on IDEAS

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    1. Modarres, Reza, 2002. "Efficient nonparametric estimation of a distribution function," Computational Statistics & Data Analysis, Elsevier, vol. 39(1), pages 75-95, March.
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    Cited by:

    1. Peng, Hanxiang & Schick, Anton, 2005. "Efficient estimation of linear functionals of a bivariate distribution with equal, but unknown marginals: the least-squares approach," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 385-409, August.
    2. Reza Modarres, 2008. "Tests of Bivariate Exchangeability," International Statistical Review, International Statistical Institute, vol. 76(2), pages 203-213, August.

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