Nonparametric estimation of the shape functions and related asymptotic results

Abstract Arriaza et al (Metrika 82:99–124, 2019) introduced the right and left shape functions, which enjoy interesting properties in terms of describing global form a distribution. This paper proposes studies nonparametric estimators those functions. The involve estimation quantile density Pointwise uniform consistency are proved under general regularity assumptions, as well limit law. Simulations included to study practical performance proposed estimators. analysis real data set illustrates methodology.