Testing for One-Sided Alternatives in Nonparametric Censored Regression

• Activity Number: 670
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Juan-Carlos Pardo-Fernandez*+ and Cedric Heuchenne
• Companies: Universidade de Vigo and Universite de Liege
• Keywords: Bootstrap ; Comparison of regression curves ; Nonparametric regression ; Regression residuals ; Right censoring

Abstract

Consider two bivariate populations. In each population, the first variable is identified with a covariate and the second variable is identified with the response of a general nonparametric and heteroscedastic regression model. We assume that the response variable is subject to right censoring. In this talk, we will propose a procedure to test the null hypothesis of equality of the regression functions versus one-sided alternatives, that is, the regression function in the first population is less than the regression function in the second population. We introduce two test statistics for which we obtain the asymptotic normality under the null and the alternative hypotheses. Although the tests are based on nonparametric techniques, they can detect any local alternative converging to the null hypothesis at the parametric rate. The practical performance of a bootstrap version of the tests is investigated in a simulation study. An application to a data set about unemployment duration times illustrates the proposed methodology.