r-(k,d) sınıf tahmin edicisinin, ortalama karesel hata kriterine göre bazı yanlı tahmin ediciler ile karşılaştırılması

Year 2018, Volume 11, Issue 1, 13 - 22, 29.06.2018

Nilgün YILDIZ

Abstract

En küçük kareler, temel bileşenler ve Liu-tipi tahmin ediciler, çok değişkenli regresyon modelleri için r-(k,d) sınıf tahmin edicilerin özel durumlarıdır.Bu makalede r-(k,d) sınıf tahmin edicisini, en küçük kareler, temel bileşenler ve Liu-tipi tahmin ediciler ile Matris Hata kareler ortalaması kriterine göre karşılaştırılmıştır. Son olarak teorik sonuçları göstermek için sayısal bir örnek ve bir Monte Carlo simülasyonu verilmektedir.Comparison of the   class estimators to some estimators by the mean square error matrix criteria

Keywords

Liu-tipi tahmin edici, r-(k, d )Sınıf Tahmin Edici, Temel bileşenler regresyonu, Matris Hata Kareler Ortalaması, Çoklu İç İlişki

Comparison of the class estimators to some estimators by the mean square error matrix criteria

Abstract

 The ordinary leastsquares, the principal components regression and the Liu-type estimators are special cases of ther-(k,d)class estimators, for regression models with multicollinearity. In thisa rticle we derived conditions for the superiority of ther-(k,d) classestimatoroverotherestimatorssuch as ordinaryleastsquares, principalcomponentandLiu-typeestimatorbased on the mean square error matrix(MSEM)criterion. Finally, a numericale xample and a Monte Carlo simulation are also given to show the theoretical results.

Keywords

Liu-type estimators;r-(k, d) class estimator, Principal Component Regression, Mean square error matrix

References

• [1] C. Stein, 1956, Inadmissibility of the usual estimator for mean of multivariate normal distribution. In Neyman J (ed),Proceedings of the third Berkley symposium on mathematical and statistics probability 1, 197–206.
• [2] D.Inan 2015, Combining the Liu-type estimator and the principal component regression estimator, Statistical Papers 56,147-156.
• [3] C. Rao, H. Toutenburg, 1995, Linear Models: Least Squares and Alternatives. New York:Springer-Verlag Inc.
• [4] G.Trenkler, 1985, Mean Square Error Matrix Comparisons of Estimators in Linear Regression. Communications in Statistics Theory and MethodsA, 14, 2495–2509.
• [5] G.Trenkler, H. Toutenburg, 1990, Mean squared error matrix comparisons between biased estimators an overview of recent results,Statistical Papers,31,165–179.
• [6] J.K.Baksalary, G. Trenkler, 1991. Nonnegative and positive definiteness of matrices modified by two matrices of rank one,Linear Algebra and Its Application 151,169–184.
• [7]H.Woods, , H.H. Steinour, H.R. Starke, 1932. Effect of composition of Portland cement on heat evolved during hardening, Industrial and Engineering Chemistry 24, 1207–1214.
• [8] S.Kaçıranlar, S.Sakallioglu, F.Akdeniz, G.P.H.Styan, H.J. Werner, 1999, A new biased estimator in linear regression and a detailed analysis of the widely-analysed dataset on Portland Cement,Sankhya Indian J Stat 61(B),443–459.
• [9]K. Liu, 2003, Using Liu-type estimator to combat collinearity,Communications in Statistics Theory and Methods 32, (5),1009–1020.
• [10] B.M.G.Kibria, 2003, Performance of some new ridge regression estimators, Communications in Statistics - Simulation and Computation, 32,2389-2413.