Combining the Liu Estimator and the Principal Component Regression Estimator

Abstract

In this paper we introduce a class of estimators which includes the ordinary least squares (OLS), the principal components regression (PCR) and the Liu estimator (1). In particular, we show that our new estimator is superior, in the scalar meansquared error (mse) sense, to the Liu estimator, to the OLS estimator and to the PCR estimator.

Combining two-parameter and principal component regression estimators

“…Then the experiment is replicated 1000 times by generating new error terms. Following Kaciranlar and Sakallioglu (2001), we choose r to be the number of eigenvalues greater than unity. Then, the estimated MSE for each estimatorβ is calculated respectively as follows:…”

“…Baye and Parker (1984) proposed the r − k class estimator by combining the RR estimator and the PCR estimator into a single estimator and showed that the new estimator is better than the PCR estimator by the mean squared error (MSE) criterion. Alternatively, Kaciranlar and Sakallioglu (2001) introduced the r − d class estimator which is the combination of the Liu estimator and the PCR estimator. Batah et al (2009) obtained the modified r − k class ridge regression (MCRR) estimator by modifying the URR estimator in the line of the PCR estimator.…”

Efficiency of a stochastic restricted two-parameter estimator in linear regression

“…Beside the two estimators, some other biased estimators as ones of remedies were put forward in the literature such as ridge-2 estimator [3], r À k class estimator [4][5], r À d class estimator [6], two-parameter estimator by Sakallıoglu and Kaçiranlar [7] and alternative two-parameter estimator by Özkale and Kaçiranlar [8].…”

A Note on the Performance of Biased Estimators with Autocorrelated Errors

“…Liu [7] gave an estimator by combining the advantages of the stein and ORRE, known as Liu estimator (LE). Kaçiranlar and Sakallıoglu [8] proposed − class estimator which is a combination of the LE and PCRE and showed the superiority of the − class estimator over the OLSE, LE, and PCRE.Özkale and Kaçıranlar [9] proposed two-parameter estimator (TPE) by utilizing the advantages of the ORRE and LE and obtained necessary and sufficient condition for dominance of the TPE over the OLSE in MSE matrix sense. Further, Yang and Chang [10] also combined the ORR and Liu estimator in a different way and introduced an another two-parameter estimator (ATPE) and 2 International Journal of Mathematics and Mathematical Sciences derived necessary and sufficient conditions for superiority of the ATPE over OLSE, ORRE, LE, and TPE under MSE matrix criterion.Özkale [11] put forward a general class of estimators, − ( , ) class estimator which is a mingle of the TPE [9] and PCRE; they evaluated the performance of the − ( , ) class estimator under MSE criterion.…”