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Partially linear additive model is useful in statistical modelling as a multivariate nonparametric fitting technique. This paper considers statistical inference for the semiparametric model in the presence of multicollinearity. Based on the profile least-squares approach, we propose a novel principal components regression estimator for the parametric component, and provide the asymptotic bias and covariance matrix of the proposed estimator. Some simulations are conducted to examine the performance of our proposed estimators and the results are satisfactory.

Principal Components Regression Estimation in Semiparametric Partially Linear Additive Models