Dear Colleagues,

Multiple linear regression models play an important role in statistical inference and are used extensively in business, industry, physical, and social sciences. In this model, it is general practice to assume that explanatory variables are independent. However, in practice, there may be strong or near-strong linear relationships among the explanatory variables. In that case, independence assumptions are no longer valid, which causes the problem of multicollinearity. In the presence of multicollinearity, it is very difficult to estimate the unique effects of individual variables in the regression equation. Moreover, the estimated regression coefficients will have large sampling variances which affect both valid inference and prediction. Multicollinearity is a common problem in the field of engineering, economics, social sciences, and physical sciences. Ridge regression is one of the most useful techniques to solve the problem of multicollinearity. The performance of ridge regression (RR) estimators depends on the value of ridge parameter k. Liu (1993) suggested another shrinkage estimator where the parameter has the benefit of being a linear function of the shrinkage parameter d. Due to this advantage over ridge regression, the Liu estimator has been applied and studied by many researchers.

This Special Issue will focus on the estimation of Ridge parameter k and shrinkage estimator d, as well as preliminary and shrinkage estimation for the ridge regression and Liu regression models.

Special issue topics include (but are not limited to):

Estimation of the ridge parameter k for both linear and nonlinear regression models

Estimation of the ridge parameter k for restricted linear and nonlinear regression models

Statistical inference (confidence interval and hypothesis testing) about the ridge parameter k

Pre-test and shrinkage estimation for Ridge regression model

Estimation of the shrinkage parameter d for both linear and nonlinear regression models

Estimation of the shrinkage parameter d for restricted linear and nonlinear regression models

Statistical Inference (confidence interval and hypothesis testing) about the shrinkage parameter d

Pre-test and shrinkage estimation for Liu regression model

Prof. Dr. B. M. Golam Kibria
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Stats is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• linear model
• ridge regression
• Liu estimator
• shrinkage estimation
• MSE
• simulation study