Local least absolute relative error estimating approach for partially linear multiplicative model

Abstract

The partially linear multiplicative regression model is considered in this paper. This model, which becomes partially linear regression model after taking logarithmic transformation, is useful in analyzing data with positive responses. ? mentioned that in many practical applications the size of relative error, rather than that of error itself, is the central concern of the practitioners. First, we extend the criterion of least absolute relative error (LARE) to the partially linear multiplicative regression model by local smoothing techniques. The consistency and asymptotic normality are investigated. We also utilize random weighting method to estimate asymptotic covariance of the parameter estimator. Secondly, we propose an interesting, simple and efiective variable selection method to select important variables in linear part. The oracle property (?) is proved. Some numerical studies are conducted to evaluate and compare the performance of the proposed estimators. The body fat dataset is analyzed for illustration.