TWO-STAGE ESTIMATION FOR SEEMINGLY UNRELATED NONPARAMETRIC REGRESSION MODELS∗

Abstract This paper is concerned with the estimating problem of seemingly unrelated (SU) non-parametric regression models. The authors propose a new method to estimate the unknown functions, which is an extension of the two-stage procedure in the longitudinal data framework. The authors show the resulted estimators are asymptotically normal and more efficient than those based on only the in-dividual regression equation. Some simulation studies are given in support of the asymptotic results. A real data from an ongoing environmental epidemiologic study are used to illustrate the proposed procedure. Key words Asymptotic normality, nonparametric model, seemingly unrelated regression, two-stage estimation.