Efficient estimation of seemingly unrelated additive nonparametric regression models

This paper is concerned with the estimating problem of seemingly unrelated (SU) nonparametric additive regression models. A polynomial spline based two-stage efficient approach is proposed to estimate the nonparametric components, which takes both of the additive structure and correlation between equations into account. The asymptotic normality of the derived estimators are establishedi. The authors also show they own some advantages, including they are asymptotically more efficient than those based on only the individual regression equation and have an oracle property, which is the asymptotic distribution of each additive component is the same as it would be if the other components were known with certainty. Some simulation studies are conducted to illustrate the finite sample performance of the proposed procedure. Applying the proposed procedure to a real data set is also made.