Abstract Biased estimation methods like ridge regression, Liu‐type regression, two‐parameter regression and principal component regression have become very popular in the analysis of applied researches for health, economics, chemometrics, and social sciences in recent years. A dataset in such applied fields tends to be characterized by many independent variables on relatively fewer observations. In addition, there is a high degree of near collinearity among the explanatory variables. It is common knowledge that under these conditions, ordinary least squares estimations of regression coefficients may be very unstable, leading to very poor prediction accuracy. The aim of this article is to examine the performance of the combination of principal components regression and some biased regression estimators such as ridge, Liu and two‐parameter estimators. For this reason, a real‐life application is presented in which different selection methods of the biasing parameters are employed.

Abstract Fixed censorship is usually encountered in medical fields, as well as biological, econometric, and engineering researches. It is quite possible to come across censored data with multicollinearity in real‐life studies. The multicollinearity affects traditional Tobit maximum likelihood estimation, which is often used in presence of censored data. Biased estimators such as Tobit Liu estimator with one biasing parameter can be used for solving the multicollinearity. In this study, Tobit two‐parameter estimator with two biasing parameters is proposed as an alternative to the classical Tobit maximum likelihood and Tobit Liu estimators for the censored data. This new estimator provides advantages from two different aspects thanks to having two biasing parameters. With a simulation study consisting of several scenarios where various levels of factors like the number of independent variables, sample size, correlation degree, variance, and censorship are examined, an in‐depth experimental analysis is conducted. In these scenarios, two different biasing parameters' selection methods where one of the biasing parameters is fixed to determine the other one are used and their corresponding outputs are obtained. In addition, a real‐life application is carried out with the National Health and Nutrition Examination Survey public‐use dataset which includes some demographic and health‐related laboratory measurements. The simulation study and data analysis results show that the proposed estimator is more advantageous to its competitors.

Abstract Two‐parameter estimators have increasing usage in the linear regression model concerning mitigating the problem of multicollinearity. In this type of biased estimators, two different parameters contribute to the solution of two different problems. Previously defined two‐parameter ridge estimator (TPRE) assures considerable merits in this context. This estimator eliminates unfavorable effects of multicollinearity as well as improves the coefficient of multiple determination for the linear regression model. Concerning the TPRE, both the mean square error comparisons and some conventional selection methods for the biasing parameters are available in the literature. In this article, we mainly focus on the simultaneous estimation of the biasing parameters of the TPRE through some new optimization techniques by genetic algorithm. To observe validation of the new approaches, we perform a numerical example in addition to a Monte Carlo study. The outcomes of these runnings prove the dominance of the new approaches in comparison to existing techniques in the literature.