Nonparametric estimation of the shape functions and related asymptotic results
In: Statistical papers, Band 65, Heft 3, S. 1575-1611
ISSN: 1613-9798
AbstractArriaza et al (Metrika 82:99–124, 2019) introduced the right and left shape functions, which enjoy interesting properties in terms of describing the global form of a distribution. This paper proposes and studies nonparametric estimators of those functions. The estimators involve nonparametric estimation of the quantile and density functions. Pointwise and uniform consistency are proved under general regularity assumptions, as well as the limit in law. Simulations are included to study the practical performance of the proposed estimators. The analysis of a real data set illustrates the methodology.