The aim of this paper is to base robust inference about a shape parameter indexing a composite transformation model on a quasi- prole likelihood ratio test statistic. First, a general procedure is presented in order to construct a bounded prole estimating function for shape parameters. This method is based on a standard truncation argument from the theory of robustness. Hence, a quasi-likelihood test is derived. Numerical studies and applications to real data show that its use reveals extremely powerful, leading to improved inferences with respect to classical robust Wald and score-type test statistics
