Liu estimator in linear regression model

Multicollinearity are an important problem in multiple linear regression models. Many solutions have been proposed to solve this problem. The most important of these methods is to use biased estimation methods, which keep all the independent variables in the model and are an alternative to the least squares method. Many biased estimation methods have been studied in the literature, and the most well-known one is the ridge regression estimator defined by Hoerl and Kennard's (1970a, b). The ridge regression estimator and many different estimators and its properties have been widely studied in the literature and still continue to be studied. However, one of the most important problems about the ridge estimator is the selection of the biasing parameter. The biasing parameter of ridge estimator is not a linear function, which complicates the selection process. Therefore, the search for alternative methods to the ridge estimator has also been an important problem in regression. Many different estimation methods have been proposed in this regard, and one of the estimators that has an important place in the literature is the Liu estimator defined by Liu (1993). Liu estimator and many estimators related to this estimator have been defined in the literature, and some of their properties have been examined and continue to be examined. For this reason, in this study, the Liu estimator and the estimators defined based on Liu estimator are discussed in the linear regression model in order to shed light on future studies. For this purpose, the studies carried out between 1993-2024 were analyzed and examined in detail.