Title: Goodness-of-fit tests for regression models with a doubly truncated response
Authors: Jacobo de Una-Alvarez - University of Vigo (Spain) [presenting]
Abstract: In Survival Analysis, Epidemiology or Reliability, among other fields, doubly truncated data may appear. Double truncation means that the target variable is observed only when it falls within two random limits, which are also available in such a case. Unlike other phenomena of data incompleteness, nonparametric maximum-likelihood estimation with doubly truncated data does not have a closed form; this results in complicated asymptotics. An omnibus goodness-of-fit test for a regression model with a doubly truncated response will be introduced. The test statistic will be based on the distance between two empirical integrated regression functions: one purely nonparametric, and the other one driven by the model to be tested. The underlying process will be a marked empirical process based on weighted residuals, where the weights remove the observational bias induced by the double truncation. The asymptotic null distribution of the test statistic will be obtained for both a fully specified and a parametric regression model. A bootstrap algorithm will be proposed in order to approximate the null distribution of the test in practice. The method will be illustrated with both simulated and real data.