The Restricted and Unrestricted Two-Parameter Estimators

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].…”

Fitting Characteristics of the Two-Parameter Estimator in Linear Regression

“…Ozkale and Kaciranlar(2007) [7] introduced the TP estimator So we expect that the TP estimator has advantages over the ridge estimator.…”

“…Considering the shrinkage selected by existing methods for ridge regression may not fully address the ill conditioning problem when exists severe multicollinearity, Liu (2003) proposed the Liu-Type estimator, which can fully deal with the ill conditioning problem [6]. introduced the two-parameter (TP) estimator for the vector of parameters in a linear regression model [7]. Yang and Chang (2010) proposed a new two-parameter estimator which includes the ordinary least squares (OLS) estimator, the ridge regression (RR) estimator and the Liu estimator as special case [8].…”

A Note on the Performance of Biased Estimators with Autocorrelated Errors

“…The scalar MSE of the − ( , ) class estimator can be obtained by taking trace of the MSE matrix in (9), which is given as…”

“…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. Chang and Yang [12] suggested another general class of estimators by merging the PCRE and ATPE [10] named as principal component twoparameter estimator (PCTPE) and analyzed its performance under MSE matrix sense.…”