Let F, G be a pair of absolutely continuous cumulative distributions, where F is the distribution of interest and G is assumed to be known. The composition G−1 ◦F, which is referred to as the generalised hazard function of F with respect to G, provides a flexible framework for statistical inference of F under shape restrictions, determined by G, which enables the generalisation of some well-known models, such as the increasing hazard rate family. This paper is concerned with the problem of testing the null hypothesis H0: “G−1 ◦ F is convex”. The test statistic is based on the distance between the empirical distribution function and a corresponding isotonic estimator, which is denoted as the greatest relatively-convex minorant of the empirical distribution with respect to G. Under H0, this estimator converges uniformly to F, giving rise to a rather simple and general procedure for deriving families of consistent tests, without any support restriction. As an application, a goodness-of-fit test for the increasing hazard rate family is provided.

(2022). Testing convexity of the generalised hazard function [journal article - articolo]. In STATISTICAL PAPERS. Retrieved from http://hdl.handle.net/10446/201092

Testing convexity of the generalised hazard function

Lando, Tommaso
2022-01-06

Abstract

Let F, G be a pair of absolutely continuous cumulative distributions, where F is the distribution of interest and G is assumed to be known. The composition G−1 ◦F, which is referred to as the generalised hazard function of F with respect to G, provides a flexible framework for statistical inference of F under shape restrictions, determined by G, which enables the generalisation of some well-known models, such as the increasing hazard rate family. This paper is concerned with the problem of testing the null hypothesis H0: “G−1 ◦ F is convex”. The test statistic is based on the distance between the empirical distribution function and a corresponding isotonic estimator, which is denoted as the greatest relatively-convex minorant of the empirical distribution with respect to G. Under H0, this estimator converges uniformly to F, giving rise to a rather simple and general procedure for deriving families of consistent tests, without any support restriction. As an application, a goodness-of-fit test for the increasing hazard rate family is provided.
articolo
6-gen-2022
Lando, Tommaso
(2022). Testing convexity of the generalised hazard function [journal article - articolo]. In STATISTICAL PAPERS. Retrieved from http://hdl.handle.net/10446/201092
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/201092
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