Estimation of a star-shaped distribution function

Hammou El Barmi, Ganesh Malla and Hari Mukerjee

Journal of Nonparametric Statistics, 2017, vol. 29, issue 1, 22-39

Abstract: A life distribution function (DF) F is said to be star-shaped if $ F(x)/x $ F(x)/x is nondecreasing on its support. This generalises the model of a convex DF, even allowing for jumps. The nonparametric maximum likelihood estimation is known to be inconsistent. We provide a uniformly strongly consistent least-squares estimator. We also derive the convergence in distribution of the estimator at a point where $ F(x)/x $ F(x)/x is increasing using the arg max theorem.

Date: 2017
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DOI: 10.1080/10485252.2016.1239827

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