B-spline Speckman Estimator of Partially Linear Model
International Journal of Systems Science and Applied Mathematics
Volume 4, Issue 4, December 2019, Pages: 53-59
Received: Aug. 25, 2019; Accepted: Dec. 31, 2019; Published: Feb. 3, 2020
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Authors
Sayed Meshaal El-sayed, Department of Applied Statistics and Econometrics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt
Mohamed Reda Abonazel, Department of Applied Statistics and Econometrics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt
Mohamed Metwally Seliem, Department of Applied Statistics and Econometrics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt
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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.
Keywords
Kernel Smoothing, Monte Carlo Simulation, Penalized B-spline Estimation, Semiparametric Regression, Spline Smoothing
To cite this article
Sayed Meshaal El-sayed, Mohamed Reda Abonazel, Mohamed Metwally Seliem, B-spline Speckman Estimator of Partially Linear Model, International Journal of Systems Science and Applied Mathematics. Vol. 4, No. 4, 2019, pp. 53-59. doi: 10.11648/j.ijssam.20190404.12
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Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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