Title: Specification tests in semiparametric transformation models - a multiplier bootstrap approach,
Abstract: We consider semiparametric transformation models, where after pre-estimation
of a parametric transformation of the response the data are modeled by means of
nonparametric regression. We suggest subsequent procedures for testing
lack-of-fit of the regression function and for significance of covariables,
which - in contrast to procedures from the literature - are asymptotically not
influenced by the pre-estimation of the transformation. The test statistics are
asymptotically pivotal and have the same asymptotic distribution as in
regression models without transformation. We show validity of a multiplier
bootstrap procedure which is easier to implement and much less computationally
demanding than bootstrap procedures based on the transformation model. In a
simulation study we demonstrate the superior performance of the procedure in
comparison with the competitors from the literature.