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We consider a linear model which can have a large number of explanatoryvariables, the errors with an asymmetric distribution or some values of theexplained variable are missing at random. In order to take in account theseseveral situations, we consider the non parametric empirical likelihood (EL)estimation method. Because a constraint in EL contains an indicator functionthen a smoothed function instead of the indicator will be considered. Twosmoothed expectile maximum EL methods are proposed, one of which willautomatically select the explanatory variables. For each of the methods weobtain the convergence rate of the estimators and their asymptotic normality.The smoothed expectile empirical log-likelihood ratio process followasymptotically a chi-square distribution and moreover the adaptive LASSOsmoothed expectile maximum EL estimator satisfies the sparsity property whichguarantees the automatic selection of zero model coefficients. In order toimplement these methods, we propose four algorithms.

Smoothed empirical likelihood estimation and automatic variable  selection for an expectile high-dimensional model with possibly missing  response variable