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Year 2024, Volume: 5 Issue: 1, 25 - 35, 31.01.2024

Özge Kuran

Abstract

References

  • [1] Dawoud I., Abonazel M.R., Awwad F.A., Generalized Kibria-Lukman estimator: Method, simulation, and application, Frontiers in Applied Mathematics and Statistics, 8, 1-6, 2022.
  • [2] Eurostat website, Greenhouse gas emissions by source sector (Source:EEA, env_air_gge), https://ec.europa.eu/eurostat/cache/metadata/en/env_air_gge_esms.htm, Accessed 2018.
  • [3] Gilmour A.R., Thompson R., Cullis B.R., Average information REML: an efficient algorithm for variance parameter estimation in linear mixed models, Biometrics, 51(4), 1440-1450, 1995.
  • [4] Henderson C.R., Estimation of genetic parameters, Annals of Mathematical Statistics, 21, 309-310, 1950.
  • [5] Henderson C.R., Kempthorne O., Searle S.R., Von Krosig C.N., Estimation of environmental and genetic trends from records subject to culling, Biometrics, 15(2), 192-218, 1959.
  • [6] Hoerl A.E., Kennard R.W., Ridge regression: Biased estimation for nonorthogonal problems, Technometrics, 12(1), 55-67, 1970.
  • [7] Kaçıranlar S., Sakallıoğlu S., Akdeniz F., Styan G.P.H., Werner H.J., A new biased estimator in linear regression and a detailed analysis of the widely analyzed dataset on Portland cement, Sankhya The Indian Journal of Statistics, 61(3), 443-459, 1999.
  • [8] Kass R.E., Raftery A.E., Bayes factors, Journal of the American Statistical Association, 90(430), 773-795, 1995.
  • [9] Kibria B.M.G., Lukman A.F., A new ridge-type estimator for the linear regression model: Simulations and applications, Scientifica, Article ID 9758378, 2020.
  • [10] Liu K.J., A new class of biased estimate in linear regression, Communications in Statistics-Theory and Methods, 22(2), 393-402, 1993.
  • [11] Liu X.-Q., Hu P., General ridge predictors in a mixed linear model, Statistics, 47(2), 363-378, 2013.
  • [12] Lukman A.F., Amin M., Kibria B.M.G., K-L estimator for the linear mixed models: Computation and simulation, Concurrency and Computation: Practice and Experience, 34(6), e6780, 2022.
  • [13] Özkale M.R., Can F., An evaluation of ridge estimator in linear mixed models: An example from kidney failure data, Journal of Applied Statistics, 44(12), 2251-2269, 2017.
  • [14] Özkale M.R., Kaçıranlar S., The restricted and unrestricted two-parameter estimators, Communications in Statistics-Theory and Methods, 36(15), 2707-2725, 2007.
  • [15] Özkale M.R., Kuran Ö., A further prediction method in linear mixed models: Liu prediction, Communications in Statistics - Simulation and Computation, 49(12), 3171-3195, 2020.
  • [16] Pereira L.N., Coelho P.S., A small area predictor under area-level linear mixed models with restrictions, Communications in Statistics-Theory and Methods, 41(13-14), 2524-2544, 2012.
  • [17] Robinson G.K., That BLUP is a good thing: The estimation of random effects, Statistical Science, 6(1), 15-51, 1991.
  • [18] Searle S.R., Matrix Algebra Useful for Statistics, John Wiley and Sons, 1982.
  • [19] Štulajter F., Predictions in nonlinear regression models, Acta Mathematica Universitatis Comenianae, 66(1), 71-81, 1997.
  • [20] Swindel B.F., Good ridge estimators based on prior information, Communications in Statistics-Theory and Methods, 5(11), 1065-1075, 1976.
  • [21] Yang H., Ye H., Xue K., A further study of predictions in linear mixed models, Communications in Statistics-Theory and Methods, 43(20), 4241-4252, 2014.

Generalized Kibria-Lukman Prediction Approximation in Linear Mixed Models

Year 2024, Volume: 5 Issue: 1, 25 - 35, 31.01.2024

Özge Kuran

Abstract

One of the new suggested prediction method is the Kibria-Lukman's prediction approach under multicollinearity in linear mixed models and in this article, the generalized Kibria-Lukman estimator and predictor are introduced to combat multicollinearity problem. The comparisons between the proposed generalized Kibria-Lukman estimator/predictor and several other estimators/predictors, namely the best linear unbiased estimator/predictor and Kibria-Lukman estimator/predictor are done by using the matrix mean square error criterion. Lastly, the selection of the biasing parameter is given and to demonstrate the performance of our new de ned prediction method, the greenhouse gases data analysis is made.

Keywords

Linear mixed model mean square error generalized Kibria-Lukman predictor multicollinearity

References

  • [1] Dawoud I., Abonazel M.R., Awwad F.A., Generalized Kibria-Lukman estimator: Method, simulation, and application, Frontiers in Applied Mathematics and Statistics, 8, 1-6, 2022.
  • [2] Eurostat website, Greenhouse gas emissions by source sector (Source:EEA, env_air_gge), https://ec.europa.eu/eurostat/cache/metadata/en/env_air_gge_esms.htm, Accessed 2018.
  • [3] Gilmour A.R., Thompson R., Cullis B.R., Average information REML: an efficient algorithm for variance parameter estimation in linear mixed models, Biometrics, 51(4), 1440-1450, 1995.
  • [4] Henderson C.R., Estimation of genetic parameters, Annals of Mathematical Statistics, 21, 309-310, 1950.
  • [5] Henderson C.R., Kempthorne O., Searle S.R., Von Krosig C.N., Estimation of environmental and genetic trends from records subject to culling, Biometrics, 15(2), 192-218, 1959.
  • [6] Hoerl A.E., Kennard R.W., Ridge regression: Biased estimation for nonorthogonal problems, Technometrics, 12(1), 55-67, 1970.
  • [7] Kaçıranlar S., Sakallıoğlu S., Akdeniz F., Styan G.P.H., Werner H.J., A new biased estimator in linear regression and a detailed analysis of the widely analyzed dataset on Portland cement, Sankhya The Indian Journal of Statistics, 61(3), 443-459, 1999.
  • [8] Kass R.E., Raftery A.E., Bayes factors, Journal of the American Statistical Association, 90(430), 773-795, 1995.
  • [9] Kibria B.M.G., Lukman A.F., A new ridge-type estimator for the linear regression model: Simulations and applications, Scientifica, Article ID 9758378, 2020.
  • [10] Liu K.J., A new class of biased estimate in linear regression, Communications in Statistics-Theory and Methods, 22(2), 393-402, 1993.
  • [11] Liu X.-Q., Hu P., General ridge predictors in a mixed linear model, Statistics, 47(2), 363-378, 2013.
  • [12] Lukman A.F., Amin M., Kibria B.M.G., K-L estimator for the linear mixed models: Computation and simulation, Concurrency and Computation: Practice and Experience, 34(6), e6780, 2022.
  • [13] Özkale M.R., Can F., An evaluation of ridge estimator in linear mixed models: An example from kidney failure data, Journal of Applied Statistics, 44(12), 2251-2269, 2017.
  • [14] Özkale M.R., Kaçıranlar S., The restricted and unrestricted two-parameter estimators, Communications in Statistics-Theory and Methods, 36(15), 2707-2725, 2007.
  • [15] Özkale M.R., Kuran Ö., A further prediction method in linear mixed models: Liu prediction, Communications in Statistics - Simulation and Computation, 49(12), 3171-3195, 2020.
  • [16] Pereira L.N., Coelho P.S., A small area predictor under area-level linear mixed models with restrictions, Communications in Statistics-Theory and Methods, 41(13-14), 2524-2544, 2012.
  • [17] Robinson G.K., That BLUP is a good thing: The estimation of random effects, Statistical Science, 6(1), 15-51, 1991.
  • [18] Searle S.R., Matrix Algebra Useful for Statistics, John Wiley and Sons, 1982.
  • [19] Štulajter F., Predictions in nonlinear regression models, Acta Mathematica Universitatis Comenianae, 66(1), 71-81, 1997.
  • [20] Swindel B.F., Good ridge estimators based on prior information, Communications in Statistics-Theory and Methods, 5(11), 1065-1075, 1976.
  • [21] Yang H., Ye H., Xue K., A further study of predictions in linear mixed models, Communications in Statistics-Theory and Methods, 43(20), 4241-4252, 2014.
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Özge Kuran 0000-0001-5632-001X

Publication Date January 31, 2024
Published in Issue Year 2024 Volume: 5 Issue: 1

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