Selma Toker

On the performance of two parameter ridge estimator under the mean square error criterion

Lipovetsky and Conklin [12] proposed an estimator, two parameter ridge (ridge-2) estimator, as an alternative to the ordinary least squares (OLS) and the ordinary ridge (ridge-1) estimators in the presence of multicollinearity. Lipovetsky [13] improved the two parameter model and investigated various characteristics of ridge-2 solutions. In this paper, we compare ridge-2 estimator with the OLS, ridge-1 and contraction estimators with respect to matrix mean square error (MSE) criterion. A numerical example from the literature has been analyzed to evaluate the performance of mentioned estimators in the theoretical results.

On the Restricted Liu Estimator in the Logistic Regression Model

The logistic regression model is used when the response variables are dichotomous. In the presence of multicollinearity, the variance of the maximum likelihood estimator (MLE) becomes inflated. The Liu estimator for the linear regression model is proposed by Liu to remedy this problem. Urgan and Tez and Mansson et al. examined the Liu estimator (LE) for the logistic regression model. We introduced the restricted Liu estimator (RLE) for the logistic regression model. Moreover, a Monte Carlo simulation study is conducted for comparing the performances of the MLE, restricted maximum likelihood estimator (RMLE), LE, and RLE for the logistic regression model.

Two-stage Liu estimator in a simultaneous equations model

ABSTRACT Two-stage least squares estimation in a simultaneous equations model has several desirable properties under the problem of multicollinearity. So, various kinds of improved estimation techniques can be developed to deal with the problem of multicollinearity. One of them is ridge regression estimation that can be applied at both stages and defined in Vinod and Ullah [Recent advances in regression methods. New York: Marcel Dekker; 1981]. We propose three different kinds of Liu estimators that are named by their implementation stages. Mean square errors are derived to compare the performances of the mentioned estimators and two different choices of the biasing parameter are offered. Moreover, a numerical example is given with a data analysis based on the Klein Model I and a Monte Carlo experiment is conducted.

Robust two parameter ridge M-estimator for linear regression

The problem of multicollinearity and outliers in the data set produce undesirable effects on the ordinary least squares estimator. Therefore, robust two parameter ridge estimation based on M-estimator (ME) is introduced to deal with multicollinearity and outliers in the y-direction. The proposed estimator outperforms ME, two parameter ridge estimator and robust ridge M-estimator according to mean square error criterion. Moreover, a numerical example and a Monte Carlo simulation experiment are presented.

Evaluation of Two Stage Modified Ridge Estimator and Its Performance

Biased estimation methods are more desirable than two stage least squares estimation for simultaneous equations models suffering from the problem of multicollinearity. This problem is also handled by using some prior information. Taking account of this knowledge, we recommend two stage modified ridge estimator. The new estimator can also be evaluated as an alternative to the previously proposed two stage ridge estimator. The widespread performance criterion, mean square error, is taken into consideration to compare the two stage modified ridge, two stage ridge and two stage least squares estimators. A real life data analysis is investigated to prove the theoretical results in practice. In addition, t he intervals of the biasing parameter which provide the superiority of the two stage modified ridge estimator are determined with the help of figures. The researchers who deal with simultaneous systems with multicollinearity can opt for the two stage modified ridge estimator.

Ridge estimator with correlated errors and two-stage ridge estimator under inequality restrictions

Abstract Liew (1976a) introduced generalized inequality constrained least squares (GICLS) estimator and inequality constrained two-stage and three-stage least squares estimators by reducing primal–dual relation to problem of Dantzig and Cottle (1967), Cottle and Dantzig (1974) and solving with Lemke (1962) algorithm. The purpose of this article is to present inequality constrained ridge regression (ICRR) estimator with correlated errors and inequality constrained two-stage and three-stage ridge regression estimators in the presence of multicollinearity. Untruncated variance–covariance matrix and mean square error are derived for the ICRR estimator with correlated errors, and its superiority over the GICLS estimator is examined via Monte Carlo simulation.