B-spline Speckman Estimator of Partially Linear Model

Sayed Meshaal El-sayed; Mohamed Reda Abonazel; Mohamed Metwally Seliem

doi:doi:10.11648/j.ijssam.20190404.12

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B-spline Speckman Estimator of Partially Linear Model

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

Published in International Journal of Systems Science and Applied Mathematics (Volume 4, Issue 4)

Received: 25 August 2019 Accepted: 31 December 2019 Published: 3 February 2020

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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.

Published in	International Journal of Systems Science and Applied Mathematics (Volume 4, Issue 4)
DOI	10.11648/j.ijssam.20190404.12
Page(s)	53-59
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Kernel Smoothing, Monte Carlo Simulation, Penalized B-spline Estimation, Semiparametric Regression, Spline Smoothing

References

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[6]	Abonazel, M. R., Helmy, N. & Azazy, A. (2019). The Performance of Speckman Estimation for Partially Linear Model using Kernel and Spline Smoothing Approaches. International Journal of Mathematical Archive, 10 (6):10-18.
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APA Style

Sayed Meshaal El-sayed, Mohamed Reda Abonazel, Mohamed Metwally Seliem. (2020). B-spline Speckman Estimator of Partially Linear Model. International Journal of Systems Science and Applied Mathematics, 4(4), 53-59. https://doi.org/10.11648/j.ijssam.20190404.12

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ACS Style

Sayed Meshaal El-sayed; Mohamed Reda Abonazel; Mohamed Metwally Seliem. B-spline Speckman Estimator of Partially Linear Model. Int. J. Syst. Sci. Appl. Math. 2020, 4(4), 53-59. doi: 10.11648/j.ijssam.20190404.12

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AMA Style

Sayed Meshaal El-sayed, Mohamed Reda Abonazel, Mohamed Metwally Seliem. B-spline Speckman Estimator of Partially Linear Model. Int J Syst Sci Appl Math. 2020;4(4):53-59. doi: 10.11648/j.ijssam.20190404.12

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@article{10.11648/j.ijssam.20190404.12,
  author = {Sayed Meshaal El-sayed and Mohamed Reda Abonazel and Mohamed Metwally Seliem},
  title = {B-spline Speckman Estimator of Partially Linear Model},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {4},
  number = {4},
  pages = {53-59},
  doi = {10.11648/j.ijssam.20190404.12},
  url = {https://doi.org/10.11648/j.ijssam.20190404.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20190404.12},
  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.},
 year = {2020}
}

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TY  - JOUR
T1  - B-spline Speckman Estimator of Partially Linear Model
AU  - Sayed Meshaal El-sayed
AU  - Mohamed Reda Abonazel
AU  - Mohamed Metwally Seliem
Y1  - 2020/02/03
PY  - 2020
N1  - https://doi.org/10.11648/j.ijssam.20190404.12
DO  - 10.11648/j.ijssam.20190404.12
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 53
EP  - 59
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20190404.12
AB  - 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.
VL  - 4
IS  - 4
ER  -

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Author Information

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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APA Style

Sayed Meshaal El-sayed, Mohamed Reda Abonazel, Mohamed Metwally Seliem. (2020). B-spline Speckman Estimator of Partially Linear Model. International Journal of Systems Science and Applied Mathematics, 4(4), 53-59. https://doi.org/10.11648/j.ijssam.20190404.12

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ACS Style

Sayed Meshaal El-sayed; Mohamed Reda Abonazel; Mohamed Metwally Seliem. B-spline Speckman Estimator of Partially Linear Model. Int. J. Syst. Sci. Appl. Math. 2020, 4(4), 53-59. doi: 10.11648/j.ijssam.20190404.12

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AMA Style

Sayed Meshaal El-sayed, Mohamed Reda Abonazel, Mohamed Metwally Seliem. B-spline Speckman Estimator of Partially Linear Model. Int J Syst Sci Appl Math. 2020;4(4):53-59. doi: 10.11648/j.ijssam.20190404.12

Copy | Download

@article{10.11648/j.ijssam.20190404.12,
  author = {Sayed Meshaal El-sayed and Mohamed Reda Abonazel and Mohamed Metwally Seliem},
  title = {B-spline Speckman Estimator of Partially Linear Model},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {4},
  number = {4},
  pages = {53-59},
  doi = {10.11648/j.ijssam.20190404.12},
  url = {https://doi.org/10.11648/j.ijssam.20190404.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20190404.12},
  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.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - B-spline Speckman Estimator of Partially Linear Model
AU  - Sayed Meshaal El-sayed
AU  - Mohamed Reda Abonazel
AU  - Mohamed Metwally Seliem
Y1  - 2020/02/03
PY  - 2020
N1  - https://doi.org/10.11648/j.ijssam.20190404.12
DO  - 10.11648/j.ijssam.20190404.12
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 53
EP  - 59
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20190404.12
AB  - 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.
VL  - 4
IS  - 4
ER  -

Copy | Download