Goodness‐of‐fit tests for parametric models in censored regression

Abstract

Abstract:The authors propose a goodness-of-fit test for parametric regression models when the response variable is right-censored. Their test compares an estimation of the error distribution based on parametric residuals to another estimation relying on nonparametric residuals. They call on a bootstrap mechanism in order to approximate the critical values of tests based on KolmogorovSmirnov and Cram&-von Mises type statistics. They also present the results of Monte Car10 simulations and use data from a study about quasars to illustrate their work.Tests d'ajustement pour des modeles de regression parametriques sujets a censure RbumC : Les auteurs proposent un test pennettant de juger de l'ad6quation d'un modble de rkgression parambtrique dont la variable dponse est sujette 21 une censure B droite. Leur test compare une estimation de la loi des erreurs d6duite de residus param6triques B une autre estimation fondke sur des r6sidus non param6triques. Ils font appel B une technique de dkchantillonnage pour approximer les valeurs critiques de tests fond& sur des statistiques de type KolmogorovSmirnov et Cram&-von Mises. 11s pdsentent aussi les rksultats d'une 6mde de Monte-Carlo et illustrent leur propos B l'aide de doM6es issues de travaux portant sur les quasars.

Nonparametric lack-of-fit tests for parametric mean-regression models with censored data

“…Moreover, neither Stute et al [26] nor Sánchez-Sellero et al [19] studied the consistency of these tests against a sequence of alternatives approaching the null hypothesis. Pardo-Fernandez et al [18] proposed another test for parametric models in censored regression that is based on a comparison of two estimators, parametric and nonparametric, of the distribution of the errors. As the latter estimator is based on a nonparametric location-scale model, the test of Pardo-Fernandez et al [18] is not consistent against any alternative.…”

Estimation of a General Parametric Location in Censored Regression

“…They also replace the censored observations by some kind of synthetic data estimated under the assumed location-scale model. Also see Pardo-Fernández et al (2007) for a goodness-of-fit test in parametric censored regression.…”

Scale Checks in Censored Regression

“…In the censored case, González Manteiga, Heuchenne and Sánchez Sellero (2007) considered goodnessof-fit tests for the conditional mean and variance functions while Pardo Fernández, Van Keilegom and González Manteiga (2007) addressed the problem for a specific location function using the process of the difference of residuals distributions. This process has been widely studied, b.e., by Dette, Pardo Fernández and Van Keilegom (2007) or Van Keilegom, González Manteiga and Sánchez Sellero (2007).…”