A test of fit for a continuous distribution based on the empirical convex conditional mean function

M. Towhidi and M. Salmanpour

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 3, 1490-1505

Abstract: Gupta and Kirmani (2008) showed that the convex conditional mean function (CCMF) characterizes the distribution function completely. In this paper, we introduce a consistent estimator of CCMF and call it empirical convex conditional mean function (ECCMF). Then we construct a simple consistent test of fit based on the integrated squared difference between ECCMF and CCMF. The theoretical and asymptotic properties of the estimator ECCMF and the proposed test statistic are studied. The performance of the constructed test is investigated under different distributions using simulations.

Date: 2017
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DOI: 10.1080/03610926.2015.1019151

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