Estimation of a semiparametric transformation model: a novel approach based on least squares minimization (Q2293725)

The authors investigate the semi-parametric transformation model \[ \Lambda_\theta(Y) = m(X) + \epsilon \] with a \(d\)-dimensional covariate \(X\), a univariate response \(Y\) and centered error term \(\epsilon\) independent of \(X\). The regression function \(m\) is assumed to be unknown, and the authors aim to estimate the transformation parameter \(\theta \in \Theta\). Therefore they consider a fully nonparametric estimator \(\hat \Lambda\) of \(\Lambda_\theta\) (which is assumed to be strictly increasing) and analyze two estimators for \(\theta\) which arise from minimizing the \(L^2\)-distance between \(\hat \Lambda\) and the model. The difference between these two estimators consists in fixing or estimating two constants which ensure identifiability of the model. The authors establish consistency and asymptotic normality of both estimators and investigate their behavior in a simulation study.