Sieve maximum likelihood estimation in a semi-parametric regression model with errors in variables

Abstract

The paper deals with a semi-parametric regression problem under deterministic and regular design which is observed with errors. We first linearise the problem using a sieve approach and then apply the total penalised maximum likelihood estimator to the linearised model. Sufficient conditions for √n-consistency and efficiency under parametric assumption are derived and a possible misspecification bias under different smoothness assumptions on the design is analysed. The Monte Carlo simulations show the performance of the estimator with simulated data.