ABSTRACT
A life distribution function (DF) F is said to be star-shaped if 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
is increasing using the arg max theorem.
Acknowledgments
The authors are grateful to four anonymous reviewers for thorough reviews and comments, and especially to one reviewer who pointed out several mistakes in the proof of Theorem 4.1 and many other careful observations and suggestions. Hammou El Barmi acknowledges the support of the City University of New York through a PSC-CUNY grant and by Ministerio de Economia y Competitividad and FEDER under research grant MTM2013-40941-P.
Disclosure statement
No potential conflict of interest was reported by the author(s).