Estimation of a star-shaped distribution function. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: El Barmi, Hammou; Malla, Ganesh; Mukerjee, Hari
• Is Part Of: Journal of nonparametric statistics. Volume 29:Issue 1(2017)
• Page Start: 22
• Page End: 39
• Publication Date: 2017-01-02
• Subjects: Star-shaped distribution functions -- uniform consistency -- convergence in distribution -- argmax theorem; 62P10 -- 62G05 -- 62E10; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2016.1239827
• Languages: English
• ISSNs: 1048-5252

Abstract

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.