Adaptive Partially Linear Regression Models by Mixing Different Estimates
American Journal of Theoretical and Applied Statistics
Volume 8, Issue 5, September 2019, Pages: 157-168
Received: Jun. 24, 2019; Accepted: Jul. 26, 2019; Published: Sep. 4, 2019
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Author
Magda Mohamed Mohamed Haggag, Department of Statistics, Mathematics, and Insurance, Faculty of Commerce, Damanhour University, Damanhour, Egypt
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Abstract
This paper proposes adapting the semiparametric partial model (PLM) by mixing different estimation procedures defined under different conditions. Choosing an estimation method of PLM, from several estimation methods, is an important issue, which depends on the performance of the method and the properties of the resulting estimators. Practically, it is difficult to assign the conditions which give the best estimation procedure for the data at hand, so adaptive procedure is needed. Kernel smoothing, spline smoothing, and difference based methods are different estimation procedures used to estimate the partially linear model. Some of these methods will be used in adapting the PLM by mixing. The adapted proposed estimator is found to be a square root-consistent and has asymptotic normal distribution for the parametric component of the model. Simulation studies with different settings, and real data are used to evaluate the proposed adaptive estimator. Correlated and non-correlated regressors are used for the parametric components of the semiparametric partial model (PLM). Best results are obtained in the case of correlated regressors than in the non-correlated ones. The proposed adaptive estimator is compared to the candidate model estimators used in mixing. Best results are obtained in the form of less risk error and less convergence rate for the proposed adaptive partial linear model (PLM).
Keywords
Backfitting Method, Combining Regression Procedures, Difference Based Method, Partially Linear Models, Profile Likelihood Method, Semiparametric Regression, Spline Smoothing
To cite this article
Magda Mohamed Mohamed Haggag, Adaptive Partially Linear Regression Models by Mixing Different Estimates, American Journal of Theoretical and Applied Statistics. Vol. 8, No. 5, 2019, pp. 157-168. doi: 10.11648/j.ajtas.20190805.11
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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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