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In this note, we make some comments about the paper of Alheety and Kibria (2014) and correct the wrongly proved Theorems in that paper. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two new classes of estimators called the stochastic restricted almost unbiased ridge-type principal component estimator (SRAURPCE) and the stochastic restricted almost unbiased Liu-type principal component estimator (SRAURPCE) to overcome the well-known multicollinearity problem in linear regression model. For the two cases when the restrictions are true and not true, necessary and sufficient conditions for the superiority of the proposed estimators are derived and compared, respectively. Furthermore, a Monte Carlo simulation study and a numerical example are given to illustrate the performance of the proposed estimators. [ABSTRACT FROM AUTHOR]

Multiple linear regression models are frequently used in predicting unknown values of the response variabley. In this case, a regression model's ability to produce an adequate prediction equation is of prime importance. This paper discusses the predictive performance of ther-kandr-dclass estimators compared to ordinary least squares (OLS), principal components, ridge regression and Liu estimators and between each other. The theoretical results are illustrated using Portland cement data and a region is established where ther-kand ther-dclass estimators are uniformly superior to the other mentioned estimators. [ABSTRACT FROM AUTHOR]

In regression analysis, to deal with the problem of multicollinearity, the restricted principal components regression estimator is proposed. In this paper, we compared the restricted principal components regression estimator, the principal components regression estimator, and the ordinary least-squares estimator with each other under the Pitman's closeness criterion. We showed that the restricted principal components regression estimator is always superior to the principal components regression estimator, under certain conditions the restricted principal components regression estimator is superior to the ordinary least-squares estimator under the Pitman's closeness criterion and under certain conditions the principal components regression estimator is superior to the ordinary least-squares estimator under the Pitman's closeness criterion. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce a new restricted two-parameter (RTP) estimator for the vector of parameters in a linear model when additional linear restrictions on the parameter vector are assumed to hold. We show that our new biased estimator is superior in the matrix mean square error criterion to the restricted ridge estimator proposed by Groß (2003), restricted Liu estimator introduced by Kaçiranlar et al. (1999), and RTP estimator introduced by Özkale and Kaçiranlar (2007). A numerical example and a Monte Carlo simulation have been analyzed to illustrate some of the theoretical results. [ABSTRACT FROM PUBLISHER]