On the use of nonparametric regression techniques for fitting parametric regression models

A new method for fitting parametric regression models is proposed. It consists of applying the least squares (LS) principle on the pairs (x(i), m(x(i))), i = 1,..., n, where X denotes the explanatory variable and m(x) is a location estimate of the conditional distribution of the response variable Y given that X = x. Consistency and asymptotic normality of the estimators are established under general conditions. These conditions are shown to be satisfied when the data are incomplete due to random censoring or truncation. Usable expressions for the asymptotic variance covariance matrix of the parameters are provided in these incomplete data cases. As an extra bonus, this regression method allows the use of ordinary residual plots as a data- analytic aide. This is illustrated on two real data sets. A simulation study examines the small sample behavior of the estimators and their estimated asymptotic variance. Extension of the method to more complicated models is discussed.