B-spline Speckman Estimator of Partially Linear Model

Mohamed Reda Abonazel,Mohamed Metwally Seliem,Sayed Meshaal El-Sayed

doi:10.11648/j.ijssam.20190404.12

Mohamed Reda Abonazel, Mohamed Metwally Seliem + Show 1 more

Open Access

https://doi.org/10.11648/j.ijssam.20190404.12

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Abstract

The partially linear model (PLM) is one of semiparametric regression models; since it has both parametric (more than one) and nonparametric (only one) components in the same model, so this model is more flexible than the linear regression models containing only parametric components. In the literature, there are several estimators are proposed for this model; where the main difference between these estimators is the estimation method used to estimate the nonparametric component, since the parametric component is estimated by least squares method mostly. The Speckman estimator is one of the commonly used for estimating the parameters of the PLM, this estimator based on kernel smoothing approach to estimate nonparametric component in the model. According to the papers in nonparametric regression, in general, the spline smoothing approach is more efficient than kernel smoothing approach. Therefore, we suggested, in this paper, using the basis spline (B-spline) smoothing approach to estimate nonparametric component in the model instead of the kernel smoothing approach. To study the performance of the new estimator and compare it with other estimators, we conducted a Monte Carlo simulation study. The results of our simulation study confirmed that the proposed estimator was the best, because it has the lowest mean squared error.

Highlights

Linear regression modelling is a good form for linking variables because in general the parameters have some kind of meaning or interpretation
The resulting model known as partially linear model (PLM) was introduced by Engle et al [1] to study the effect of weather on electricity demand
Note that the intercept term has been omitted from the parametric component without loss of any generality, since the first point on a nonparametric regression line plays the role of an intercept

Summary

Introduction

Linear regression modelling is a good form for linking variables because in general the parameters have some kind of meaning or interpretation. . Note that the intercept term has been omitted from the parametric component without loss of any generality, since the first point on a nonparametric regression line plays the role of an intercept. This model has gained great popularity since it was first introduced by Engle et al [1] and has been widely applied in economics, social, biological sciences, and so on. For estimating the nonparametric component in the PLM, the spline smoothing approach is used in many studies, such as [1,2,3,4,5,6].

Speckman Estimator

Spline Smoothing Estimator

Proposed Estimator

Monto Carlo Simulation Study

Conclusion