Sieve extremum estimation of a semiparametric transformation model

This paper considers the estimation of a semiparametric transformation model, A(y(t), beta(0))= g(x(t))+u(t), where Lambda(., beta(0)) is a strictly increasing function known up to an l-dimensional parameter beta(0), g is an unknown link function. Hermite polynomial expansion is used to approximate the link function g, which leads to an extreme estimator for beta(0) and a plug-in estimator for g. Asymptotic properties of the estimators are established. Simulation results demonstrate that the estimators perform well in finite samples. An example on Canadian occupation prestige is provided to illustrate the practical value of the proposed model. (C) 2020 Elsevier B.V. All rights reserved.