A new class of efficient and debiased two-step shrinkage estimators: method and application.

This paper introduces a new class of efficient and debiased two-step shrinkage estimators for a linear regression model in the presence of multicollinearity. We derive the proposed estimators' mean square error and define the necessary and sufficient conditions for superiority over the existing estimators. In addition, we develop an algorithm for selecting the shrinkage parameters for the proposed estimators. The comparison of the new estimators versus the traditional ordinary least squares, ridge regression, Liu, and the two-parameter estimators is done by a matrix mean square error criterion. The Monte Carlo simulation results show the superiority of the proposed estimators under certain conditions. In the presence of high but imperfect multicollinearity, the two-step shrinkage estimators' performance is relatively better. Finally, two real-world chemical data are analyzed to demonstrate the advantages and the empirical relevance of our newly proposed estimators. It is shown that the standard errors and the estimated mean square error decrease substantially for the proposed estimator. Hence, the precision of the estimated parameters is increased, which of course is one of the main objectives of the practitioners.

Biased Adjusted Poisson Ridge Estimators-Method and Application.

Månsson and Shukur (Econ Model 28:1475-1481, 2011) proposed a Poisson ridge regression estimator (PRRE) to reduce the negative effects of multicollinearity. However, a weakness of the PRRE is its relatively large bias. Therefore, as a remedy, Türkan and Özel (J Appl Stat 43:1892-1905, 2016) examined the performance of almost unbiased ridge estimators for the Poisson regression model. These estimators will not only reduce the consequences of multicollinearity but also decrease the bias of PRRE and thus perform more efficiently. The aim of this paper is twofold. Firstly, to derive the mean square error properties of the Modified Almost Unbiased PRRE (MAUPRRE) and Almost Unbiased PRRE (AUPRRE) and then propose new ridge estimators for MAUPRRE and AUPRRE. Secondly, to compare the performance of the MAUPRRE with the AUPRRE, PRRE and maximum likelihood estimator. Using both simulation study and real-world dataset from the Swedish football league, it is evidenced that one of the proposed, MAUPRRE ( k ^ q 4 ) performed better than the rest in the presence of high to strong (0.80-0.99) multicollinearity situation.

A new Poisson Liu Regression Estimator: method and application.

This paper considers the estimation of parameters for the Poisson regression model in the presence of high, but imperfect multicollinearity. To mitigate this problem, we suggest using the Poisson Liu Regression Estimator (PLRE) and propose some new approaches to estimate this shrinkage parameter. The small sample statistical properties of these estimators are systematically scrutinized using Monte Carlo simulations. To evaluate the performance of these estimators, we assess the Mean Square Errors (MSE) and the Mean Absolute Percentage Errors (MAPE). The simulation results clearly illustrate the benefit of the methods of estimating these types of shrinkage parameters in finite samples. Finally, we illustrate the empirical relevance of our newly proposed methods using an empirically relevant application. Thus, in summary, via simulations of empirically relevant parameter values, and by a standard empirical application, it is clearly demonstrated that our technique exhibits more precise estimators, compared to traditional techniques - at least when multicollinearity exist among the regressors.