Abstarct: Nowadays‎, ‎due to the development of technology‎, ‎it has been possible to store and analyze data with a large number of variables‎: ‎but it should be noted that if the recorded variables are not significant or the number of them is high‎, ‎classical estimation techniques are ineffective and in addition to identifying and removing redundant variables‎, ‎non-classical methods for estimating model parameters should be used‎. ‎In the regression modeling‎, ‎by using penalized estimators‎, ‎we are able to select both significant variables and estimate parameters‎. ‎In this regard‎, ‎penalized group estimators can be used if the variables are grouped in such a way that all of them have to be eliminated or they should all remain in the model‎. ‎In this dissertation‎, ‎we briefly review some of the most common and applicable modern variable selection methods and investigate penalized group estimators via a series of numerical studies‎, ‎simulations‎, ‎and analysis of genomic real data and their use in logistic regression models.‎