Estimation of the Error Density in a Semiparametric Transformation Model

Abstract

Consider the semiparametric transformation model ${\Lambda }_{{\theta }_o}(Y)=m(X)+\epsilon$, where ${\theta }_o$ is an unknown finite dimensional parameter, the functions ${\Lambda }_{{\theta }_o}$ and $m$ are smooth, $\epsilon$ is independent of $X$, and $\esp(ε)=0$. We propose a kernel-type estimator of the density of the error $\epsilon$, and prove its asymptotic normality. The estimated errors, which lie at the basis of this estimator, are obtained from a profile likelihood estimator of ${\theta }_o$ and a nonparametric kernel estimator of $m$. The practical performance of the proposed density estimator is evaluated in a simulation study.

References in corpus (2)

• Uniform in bandwidth consistency of kernel-type function estimators
• Estimation of a semiparametric transformation model