Lineer Konveks Kombinasyon Tahmin Ediciler ve Karşılaştırmalar

Yıl 2021, Cilt: 11 Sayı: 2, 302 - 320, 31.12.2021

Selahattin Kaçıranlar Issam Dawoud Dünya Karapınar

https://doi.org/10.37094/adyujsci.938882

Öz

Bu makalede, en küçük kareler, ridge ve Liu tahmin ediciler gibi bilinen tahmin edicilerle öngörü performansını karşılaştırmak için iki lineer konveks kombinasyon tahmin edicisi tanımlanmıştır. Ayrıca, öngörü hata kareleri ortalaması kriterine göre bu tahmin edicilerin karşılaştırılmaları bir sayısal örnek ile incelenmiştir.

Anahtar Kelimeler

Yanlı tahmin; Ridge tahmin edici; Lineer konveks kombinasyon; Liu tahmin edici; Öngörü hata kareleri ortalaması

Linear Convex Combination Estimators and Comparisons

Öz

In this paper, we introduce two linear convex combination estimators by using known estimators such as ordinary least squares, ridge and Liu estimators and examine the predictive performance of these estimators. Furthermore, a numerical example is examined to compare these estimators under the prediction mean squared error criterion.

Anahtar Kelimeler

biased estimation, ridge estimator, linear convex combination, Liu estimator, prediction mean square error

Kaynakça

• [1] Hoerl, A.E., Kennard, R.W., Ridge regression: biased estimation for nonorthogonal problems, Technometrics, 12, 55–76, 1970.
• [2] Askın, R.G., Multicollinearity in regression: Review and examples, Journal of Forecasting, 1, 281-292, 1982.
• [3] Montgomery, D.C., Friedman, D.J., Prediction using regression models with multicollinear predictor variables, IIE Transactions, 2 (3), 73-85, 1993.
• [4] Liu, K., A new class of biased estimate in linear regression, Communications in Statistics- Theory and Methods, 22, 393-402, 1993.
• [5] Akdeniz, F., Kaçıranlar, S., On the almost unbiased generalized Liu estimator and unbiased estimation of the bias and MSE, Communications in Statistics-Theory and Methods, 24, 1789-1797, 1995.
• [6] Sakallıoğlu, S., Kaçıranlar, S., Akdeniz, F., Mean squared error comparisons of some biased regression estimator, Communications in Statistics-Theory and Methods, 30, 347-361, 2001.
• [7] Özkale, M.R., Kaçıranlar, S., The restricted and unrestricted two parameter estimators, Communications in Statistics- Theory and Methods, 36, 2707–2725, 2007.
• [8] Swindel, B.F., Good ridge estimators based on prior information, Communications in Statistics-Theory and Methods, A5, 1065–1075, 1976.
• [9] Özkale, M.R., Influence measures in affine combination type regression, Journal of Applied Statistics, 40, 2219-2243, 2013.
• [10] Theil, H., On the use of incomplete prior information in regression analysis, Journal of American Statistical Association, 58, 401–414, 1963.
• [11] Theil, H., Goldberger, A.S., On pure and mixed statistical estimation in economics, International Economic Review, 2, 65–78, 1961.
• [12] Özbay, N., Kaçıranlar, S., The Almon two parameter estimator for the distributed lag models, Journal of Statistical Computation and Simulation, 87, 834–843, 2017.
• [13] Özbay, N., Kaçıranlar, S., Estimation in a linear regression model with stochastic linear restrictions: a new two parameter-weighted mixed estimator, Journal of Statistical Computation and Simulation, 88, 1669–1683, 2018.
• [14] Schaffrin, B., Toutenburg, H., Weighted mixed regression, Zeitschrift fur Angewandte Mathematik und Mechanik, 70, 735-738, 1990.
• [15] Tekeli, E., Kaçıranlar, S., Özbay, N., Optimal determination of the parameters of some biased estimators using genetic algorithm, Journal of Statistical Computation and Simulation, 89 (18), 3331-3353, 2019.
• [16] Çetinkaya, M.K., Kaçıranlar, S., Improved two parameter estimators for the negative binomial and Poisson regression models, Journal of Statistical Computation and Simulation, 89(14), 2645-2660, 2019.
• [17] Gruber, M.H.J., Regression estimators: A comparative study. 2nd ed., John Hopkins University Press, Baltimore, MD; 2010.
• [18] Gruber, M.H.J., Liu and ridge estimators- A comparison, Communications in Statistics- Theory and Methods, 41, 3739-3749, 2012.
• [19] Mayer, L.S., Willke, T.A., On biased estimation in linear models, Technometrics, 15, 497–508, 1973.
• [20] Friedman, D.J., Montgomery, D.C., Evaluation of the predictive performance of biased regression estimators, Journal of Forecasting, 4, 153-163, 1985.
• [21] Özbey, F., Kaçıranlar, S., Evaluation of the predictive performance of the Liu estimator, Communications in Statistics-Theory and Methods, 44, 1981-1993, 2015.
• [22] Dawoud, I., Kaçıranlar, S., The predictive performance evaluation of biased regression predictors with correlated errors, Journal of Forecasting, 34, 364-378, 2015.
• [23] Dawoud, I., Kaçıranlar, S., Evaluation of the predictive performance of the r-k and r-d class estimators, Communications in Statistics-Theory and Methods, 46, 4031-4050, 2017.
• [24] Dawoud, I., Kaçıranlar, S., Evaluation of the predictive performance of the Liu-type estimator, Communications in Statistics–Simulation and Computation, 46, 2800-2820, 2017.
• [25] Liu, K., Using Liu-type estimator to combat collinearity, Communications in Statistics- Theory and Methods, 32, 1009–1020, 2003.
• [26] Li, R., Li, F., Huang, J., Evaluation of the predictive performance of the principal component two-parameter estimator, Concurrency and Computation Practice and Experince, 31, e4710, 2019. https://doi.org/10.1002/cpe.4710.
• [27] Chang, X., Yang, H., Combining two-parameter and principal component regression estimator, Statistical Papers, 53(3), 549-562, 2012.
• [28] Kibria, B.M.G., Performance of some new ridge regression estimators, Communications in Statistics–Simulation and Computation, 32, 419-435, 2003.
• [29] Khalaf, G., Shukur, G., Choosing ridge parameters for regression problems, Communications in Statistics-Theory and Methods, 34, 1177-1182, 2005.
• [30] Muniz, G., Kibria, B.M.G., On some ridge regression estimators: An empirical comparison, Communications in Statistics–Simulation and Computation, 38, 621-630, 2009.