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This paper investigates the estimation problem of semi-parametric partially linear varying-coefficient models by the technique of back-fitting. In order to avoid the disturbance of multi-collinearity and improve estimation efficiency, we apply principal component analysis to semi-parametric partially linear varying-coefficient models due to principal components are those uncorrelated linear combinations. And then we obtain the estimators of original parametric component and nonparametric component respectively. Model estimation and some statistic inferences about the property of the estimators are also derived theoretically.

Back-fitting Estimation of Semiparametric Partially Linear Varying-coefficient Models with PCA