Specification tests in semiparametric transformation models - A multiplier bootstrap approach

Semiparametric transformation models are considered, where after pre-estimation of a parametric transformation of the response the data are modeled by means of nonparametric regression. Subsequent procedures for testing lack-of-fit of the regression function and for significance of covariates are suggested. In contrast to existing procedures, the tests are asymptotically not influenced by the pre-estimation of the transformation in the sense that they have the same asymptotic distribution as in regression models without transformation. Validity of a multiplier bootstrap procedure is shown which is easier to implement and much less computationally demanding than bootstrap procedures based on the transformation model. In a simulation study the superior performance of the procedure in comparison with its existing competitors is demonstrated. (C) 2019 Elsevier B.V. All rights reserved.