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Title: Robust estimation and variable selection for regression models using empirical likelihood and LASSO methods Authors:  Senay Ozdemir - Afyon Kocatepe University (Turkey) [presenting]
Yesim Guney - Ankara University (Turkey)
Yetkin Tuac - Ankara University (Turkey)
Olcay Arslan - Ankara University (Turkey)
Abstract: There are several methods to estimate the parameters of a linear regression model. These methods are mainly based on some distributional assumptions on error terms. When these assumptions are not plausible, nonparametric methods, like empirical likelihood, can be used to deal with the estimation problem in regression analysis. Empirical likelihood method performs by maximizing an empirical likelihood function defined as the multiplication of unknown probabilistic weights for each observation under some constraints. In ordinary case, one of these constraints is similar to normal equation in ordinary least square estimation method which is drastically effected from outliers in the data. Replacing this non-robust constraint with a robust one, the empirical likelihood estimators can be made robust against the outliers in data. Another vital issue in a regression analysis is to select the significant variables. It has been mainly purposed to also carry on variable selection along with the parameter estimation in a regression analysis based on the empirical likelihood method. To this extend, we combine the LASSO (least absolute shrinkage and selection operator) method with robust empirical likelihood regression estimation to obtain robust regression estimators and select the important explanatory variables.