Ortalama Karesel Hata Matrisi Kriterine göre Yanlı Tahmin Ediciler Üzerine Çalışma

Abstract

Çoklu doğrusallığa sahip regresyon modelleri, r- (k, d) sınıfı tahmincileri, ana bileşen regresyonu, Liu tipi tahminciler gibi çeşitli tahmincileri kullanarak ele alınabilir. Bu çalışmada, r- (k, d) sınıfı kestiricisinin, ana bileşenlerin regresyonu, Liu tipi tahmincileri ve sıradan en küçük kareler üzerinde, ortalama karesel hata matrisi (MSEM) kriteri açısından üstün olduğu koşulları belirledik. Son olarak, sayısal bir örnek ve Monte Carlo simülasyonu ile teorik sonuçları gösterdik.

Keywords

• Liu-tipi tahmin edici,r-(k,d )Sınıf Tahmin Edici Temel bileşenler regresyonu,ortalama karesel hata matrisi

The Research on Biased Estimators Based on Mean Square Error Matrix Criteria

Abstract

Regression models with multicollinearity can be tackled by using various estimators such as   class estimators, principal components regression, Liu-type estimators. In this study, we defined conditions where the   class estimator is superior over the biased estimators in terms of mean square error matrix (MSEM) criterion. Finally, we showed theoretical results by means of a numerical example and a simulation study.

Keywords

• r-(k,d) class estimator,Liu-type estimators,(r-d) class estimator,Ordinary Ridge Regression Principal Component Regression,Mean square error matrix,Multicollinearity

References

1. [1] Stein, C., 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, (1956), 197–206. [2] Inan, D., Combining the Liu-type estimator and the principal component regression estimator. Statistical Papers 56, (2015), 147-156. [3] Rao, C. and Toutenburg, H., Linear Models: Least Squares and Alternatives. New York:Springer-Verlag Inc. 1995. [4] Trenkler, G., Mean Square Error Matrix Comparisons of Estimators in Linear Regression. Communications in Statistics Theory and Methods A.14,( 1985) 2495–2509. [5] Trenkler, G. and Toutenburg, H., Mean squared error matrix comparisons between biased estimators an overview of recent results, Statistical Paper 31 (1990 )165–179. [6] Baksalary, J.K. and Trenkler, G., Nonnegative and positive definiteness of matrices modified by two matrices of rank one, Linear Algebra and Its Application 151, (1991), 169–184. [7] Graybill, F.A., Theory and Application of the Linear Model. Duxbury Press, North Scituate, Massachusetts,1976. [8] Woods, H., Steinour , H.H. and Starke. H.R., Effect of composition of Portland cement on heat evolved during hardening, Industrial and Engineering Chemistry 24, (1932),1207–1214. [9] Kaçıranlar, S., Sakallioglu, S., Akdeniz, F., Styan, G.P.H. and Werner. H.J., 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),( 1999), 443–459. [10] Liu, K., Using Liu-type estimator to combat collinearity, Communications in Statistics Theory and Methods 32. (5), (2003),1009–1020. [11] Kibria. B.M.G., Performance of some new ridge regression estimators, Communications in Statistics - Simulation and Computation. 32, (2003),2389-2413.