Semiparametric estimation of regression functions under shape invariance restrictions

This paper considers the shape invariant modelling approach in semiparametric regression estimation. Nonparametric functions of similar shape are linked by parametric transformations with unknown parameters. A computationally convenient estimation procedure is suggested. √N- consistency of the parameter estimates is proved. Finite sample performance of this estimator is investigated by simulations. An application to consumer data illustrates the importance of this method for applied statistics. Estimations indicate that the imposed shape invariance restrictions have empirical evidence in the semiparametric modelling of consumer demand.