A Study of Semiparametric Additive Model Using Backfitting Algorithm

Abstract

Semiparametric density estimation is of wide applications with numerous novel approaches in its estimation. The curse of dimensionality effect which is usually associated with nonparametric density estimation is often addressed with the semiparametric density estimation. The curse of dimensionality effect in nonparametric estimation is due to the addition of more explanatory variables to a model which ultimately leads to slow convergence rate of the model. As the explanatory variables increases, the nonparametric approach in data estimation becomes difficult and hence the need for the semiparametric approach. In semiparametric estimation, the variables are considered independently in terms of their relation with the response variable through the additive techniques. This paper considers the additive model by employing the Backfitting algorithm and the kernel smoother. The Backfitting algorithm is apply on real data using the Adjusted R-Squared as the measure of performance and the results revealed dominance of the semiparametric approach over the nonparametric method. Again, the model addresses the curse of dimensionality effects that is often associated with is nonparametric counterpart.