Estimation of the error density in a semiparametric transformation model

Consider the semiparametric transformation model Λθo(Y ) = m(X) + ε, where θo is an unknown finite dimensional parameter, the functions Λθo and m are smooth, ε is independent of X, and E(ε) = 0. We propose a kernel-type estimator of the density of the error ε, and prove its asymptotic normality. The estimated errors, which lie at the basis of this estimator, are obtained from a profile likelihood estimator of θo and a nonparametric kernel estimator of m. The practical performance of the proposed density estimator is evaluated in a simulation study.status: publishe