Tests for validity of the semiparametric heteroskedastic transformation model

Abstract

There exist a number of tests for assessing the nonparametric heteroscedastic location-scale assumption. Here we consider a goodness-of-fit test for the more general hypothesis of the validity of this model under a parametric functional transformation on the response variable. Specifically we consider testing for independence between the regressors and the errors in a model where the transformed response is just a location/scale shift of the error. Our criteria use the familiar factorization property of the joint characteristic function of the covariates under independence. The difficulty is that the errors are unobserved and hence one needs to employ properly estimated residuals in their place. We study the limit distribution of the test statistics under the null hypothesis as well as under alternatives, and also suggest a resampling procedure in order to approximate the critical values of the tests. This resampling is subsequently employed in a series of Monte Carlo experiments that illustrate the finite-sample properties of the new test. We also investigate the performance of related test statistics for normality and symmetry of errors, and apply our methods on real data sets.

Characteristic function and Laplace transform‐based tests for exponentiality in the presence of random right censoring

“…Exponential θexpðÀθxÞ Exp(θ) A warp-speed bootstrap methodology (Giacomini et al, 2013), which essentially entails using a single bootstrap replication for each Monte Carlo sample generated, is employed in order to calculate empirical powers. This methodology is used in order to reduce the computational cost of the calculation of these powers and has been employed by a number of authors in the literature to compare Monte Carlo performances (see, e.g., Hušková et al, 2020).…”