Lunch Seminar Economics (LSE) - 2020/2021

Interviene: Tommaso Lando, Università di Bergamo

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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 generalized hazard function of F wrt G, provides a flexible framework for statistical inference of F under shape restrictions (determined by G), which enables the generalization of some well-known models, such as the increasing hazard rate family. This study is concerned with the problem of testing the null hypothesis H_0: ” 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 wrt to G. Under H_0, this estimator converges uniformly to F, giving rise to a rather simple and general procedure for deriving consistent tests, without any support restriction. As an application, a goodness-of-fit test for the increasing hazard rate family is provided.