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 parameters, and U has unknown cumulative distribution function F. It is not assumed that Lambda and F belong to known parametric families; they are estimated nonparametrically. This model generalizes a large number of widely used models that make stronger a priori assumptions about Lambda and/or F. The paper develops n(1/2)-consistent, asymptotically normal estimators of Lambda, F, and quantiles of the conditional distribution of Y. Estimators of beta that are n(1/2)-consistent and asymptotically normal already exist. The results of Monte Carlo experiments indicate that the new estimators work reasonably well in samples of size 100.