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2024 | OriginalPaper | Chapter

On Some Weighted Mixed Ridge Regression Estimators: Theory, Simulation and Application

Authors : Mustafa I. Alheety, Muhammad Qasim, Kristofer Månsson, B. M. Golam Kibria

Published in: Mathematical Analysis and Numerical Methods

Publisher: Springer Nature Singapore

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Abstract

Comparisons among some new types of weighted mixed regression estimators for the linear regression model under the stochastic linear restrictions have been made in this paper. The mean squared error criterion is used to examine the superiority of different weighted mixed regression estimators. A Monte Carlo simulation study and real-life application are carried out to compare the performance of these estimators for different cases. Finally, we suggest the best weighted mixed regression estimator with collinear regressors.

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Literature
1.
go back to reference Akdeniz, F., Kaçiranlar, S.: On the almost unbiased generalized Liu estimator and unbiased estimation of the bias and MSE. Commun. Stat. Theor. Methods 24(7), 1789–1797 (1995)MathSciNetCrossRef Akdeniz, F., Kaçiranlar, S.: On the almost unbiased generalized Liu estimator and unbiased estimation of the bias and MSE. Commun. Stat. Theor. Methods 24(7), 1789–1797 (1995)MathSciNetCrossRef
2.
go back to reference Alheety, M.I., Kibria, B.M.G.: On the Liu and almost unbiased Liu estimators in the presence of multicollinearity with heteroscedastic or correlated errors. Surv. Math. Appl. 4, 155–167 (2009)MathSciNet Alheety, M.I., Kibria, B.M.G.: On the Liu and almost unbiased Liu estimators in the presence of multicollinearity with heteroscedastic or correlated errors. Surv. Math. Appl. 4, 155–167 (2009)MathSciNet
3.
go back to reference Chaolin, L., Haina, J., Xinhui, S., Donglin, L.: Two Kinds of weighted biased estimators in stochastic restricted regression model. J. Appl. Math. 10, 1–10 (2014)MathSciNet Chaolin, L., Haina, J., Xinhui, S., Donglin, L.: Two Kinds of weighted biased estimators in stochastic restricted regression model. J. Appl. Math. 10, 1–10 (2014)MathSciNet
4.
go back to reference Farebrother, R.W.: Further results on the mean square error of ridge regression. J. Roy. Stat. Soc. B 38, 248–250 (1976)MathSciNetCrossRef Farebrother, R.W.: Further results on the mean square error of ridge regression. J. Roy. Stat. Soc. B 38, 248–250 (1976)MathSciNetCrossRef
5.
go back to reference Hoerl, A.E., Kennard, R.W.: Ridge regression: biased estimation for non-orthogonal problem. Technometrics 12, 55–67 (1970)CrossRef Hoerl, A.E., Kennard, R.W.: Ridge regression: biased estimation for non-orthogonal problem. Technometrics 12, 55–67 (1970)CrossRef
6.
go back to reference Hoerl, A.E., Kennard, R.W.: Ridge Regression: application for non-orthogonal problem. Technometrics 12, 69–82 (1970)CrossRef Hoerl, A.E., Kennard, R.W.: Ridge Regression: application for non-orthogonal problem. Technometrics 12, 69–82 (1970)CrossRef
7.
go back to reference Kadiyala, K.: A class of almost unbiased and efficient estimators of regression coefficients. Econ. Lett. 16(3–4), 293–296 (1984)MathSciNetCrossRef Kadiyala, K.: A class of almost unbiased and efficient estimators of regression coefficients. Econ. Lett. 16(3–4), 293–296 (1984)MathSciNetCrossRef
8.
go back to reference Kibria, B.M.G.: Performance of some new ridge regression estimators. Commun. Stat. Simul. Comput. 32(2), 419–435 (2003)MathSciNetCrossRef Kibria, B.M.G.: Performance of some new ridge regression estimators. Commun. Stat. Simul. Comput. 32(2), 419–435 (2003)MathSciNetCrossRef
9.
go back to reference Kibria, B.M.G., Banik, S.: Some ridge regression estimators and their performances. J. Mod. Appl. Stat. Methods 15(1), 206–238 (2016)CrossRef Kibria, B.M.G., Banik, S.: Some ridge regression estimators and their performances. J. Mod. Appl. Stat. Methods 15(1), 206–238 (2016)CrossRef
10.
go back to reference Kibria, B.M.G., Lukman, A.F.: A new ridge-type estimator for the linear regression model: simulations and applications. Scientifica (2020) Kibria, B.M.G., Lukman, A.F.: A new ridge-type estimator for the linear regression model: simulations and applications. Scientifica (2020)
11.
go back to reference Li, Y., Yang, H.: A new stochastic mixed ridge estimator in linear regression model. Stat. Pap. 51(2), 315–323 (2010)MathSciNetCrossRef Li, Y., Yang, H.: A new stochastic mixed ridge estimator in linear regression model. Stat. Pap. 51(2), 315–323 (2010)MathSciNetCrossRef
12.
go back to reference Liu, K.: A new class of biased estimate in linear regression. Commun. Stat. Theory Methods 22, 393–402 (1993) Liu, K.: A new class of biased estimate in linear regression. Commun. Stat. Theory Methods 22, 393–402 (1993)
13.
go back to reference Lukman, A.F., Amin, M., Kibria, B.G.: K‐L estimator for the linear mixed models: computation and simulation. Concurr. Comput. Pract. Exp. 34(6), e6780 (2022) Lukman, A.F., Amin, M., Kibria, B.G.: K‐L estimator for the linear mixed models: computation and simulation. Concurr. Comput. Pract. Exp. 34(6), e6780 (2022)
14.
go back to reference Qasim, M., Amin, M., Omer, T.: Performance of some new Liu parameters for the linear regression model. Commun. Stat.-Theor. Methods 49(17), 4178–4196 (2020)MathSciNetCrossRef Qasim, M., Amin, M., Omer, T.: Performance of some new Liu parameters for the linear regression model. Commun. Stat.-Theor. Methods 49(17), 4178–4196 (2020)MathSciNetCrossRef
15.
go back to reference Qasim, M., Månsson, K., Sjölander, P., Kibria, B.G.: A new class of efficient and debiased two-step shrinkage estimators: method and application. J. Appl. Stat. 49(16), 4181–4205 (2022)MathSciNetCrossRef Qasim, M., Månsson, K., Sjölander, P., Kibria, B.G.: A new class of efficient and debiased two-step shrinkage estimators: method and application. J. Appl. Stat. 49(16), 4181–4205 (2022)MathSciNetCrossRef
16.
go back to reference Rao, C.R., Toutenburg, H., Shalabh, Heumann, C.: Linear Models and Generalizations: Least Squares and Alternative. Springer, New York, NY, USA (2008) Rao, C.R., Toutenburg, H., Shalabh, Heumann, C.: Linear Models and Generalizations: Least Squares and Alternative. Springer, New York, NY, USA (2008)
17.
go back to reference Schaffrin, B., Toutenburg, H.: Weighted mixed regression. Zeitschrift fur Angewandte Mathematik und Mechanik 70(6), T735–T738 (1990)MathSciNet Schaffrin, B., Toutenburg, H.: Weighted mixed regression. Zeitschrift fur Angewandte Mathematik und Mechanik 70(6), T735–T738 (1990)MathSciNet
18.
go back to reference Shukur, G.: Dynamic specification and misspecification in systems of demand equations: a testing strategy for model selection. Appl. Econ. 34, 709–725 (2002) Shukur, G.: Dynamic specification and misspecification in systems of demand equations: a testing strategy for model selection. Appl. Econ. 34, 709–725 (2002)
19.
go back to reference Theil, H., Goldberger, A.S.: On pure and mixed estimation in econometrics. Int. Econ. Rev. 2, 65–78 (1961)CrossRef Theil, H., Goldberger, A.S.: On pure and mixed estimation in econometrics. Int. Econ. Rev. 2, 65–78 (1961)CrossRef
20.
go back to reference Theil, H.: On the use of incomplete prior information in regression analysis. J. Am. Stat. Assoc. 58, 401–414 (1963)MathSciNetCrossRef Theil, H.: On the use of incomplete prior information in regression analysis. J. Am. Stat. Assoc. 58, 401–414 (1963)MathSciNetCrossRef
21.
go back to reference Yalian, L., Yang, H.: A new ridge-type estimator in stochastic restricted linear regression. Statistics 45(2), 123–130 (2011)MathSciNetCrossRef Yalian, L., Yang, H.: A new ridge-type estimator in stochastic restricted linear regression. Statistics 45(2), 123–130 (2011)MathSciNetCrossRef
22.
go back to reference Yang, H., Xu, J.: An alternative stochastic restricted Liu estimator in linear regression. Stat. Pap. 50(3), 639–647 (2009)MathSciNetCrossRef Yang, H., Xu, J.: An alternative stochastic restricted Liu estimator in linear regression. Stat. Pap. 50(3), 639–647 (2009)MathSciNetCrossRef
Metadata
Title
On Some Weighted Mixed Ridge Regression Estimators: Theory, Simulation and Application
Authors
Mustafa I. Alheety
Muhammad Qasim
Kristofer Månsson
B. M. Golam Kibria
Copyright Year
2024
Publisher
Springer Nature Singapore
DOI
https://doi.org/10.1007/978-981-97-4876-1_6

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