SEMIPARAMETRIC ESTIMATION OF A REGRESSION-MODEL WITH AN UNKNOWN TRANSFORMATION OF THE DEPENDENT VARIABLE

This paper presents a method for estimating the model Lambda(Y) = beta 'X + U, where Y is a scalar, Lambda is an unknown increasing function, X is a vector of explanatory variables, beta is a vector of unknown p arameters, and U has unknown cumulative distribution function F. It is not assumed that Lambda and F belong to known parametric families; th ey are estimated nonparametrically. This model generalizes a large num ber of widely used models that make stronger a priori assumptions abou t Lambda and/or F. The paper develops n(1/2)-consistent, asymptoticall y normal estimators of Lambda, F, and quantiles of the conditional dis tribution of Y. Estimators of beta that are n(1/2)-consistent and asym ptotically normal already exist. The results of Monte Carlo experiment s indicate that the new estimators work reasonably well in samples of size 100.