High-dimensional generalizations of asymmetric least squares regression and their applications (Q510692)

This paper considers a high-dimensional linear regression model where the mean of the residuals is 0 under an asymmetric squared error loss and the regression coefficients are estimated under this asymmetric loss plus a nonnegative penalty function. An efficient algorithm is proposed to calculate the estimates of the regression coefficient, and the consistency of the estimation procedure is proved when its dimension is high for both \(L_1\) and nonconvex penalty functions. The proposed algorithm and its theoretical properties are extended to a linear regression model where the standard deviation of the residuals is a linear function of the covariates to estimate the coefficients for both mean and variance components of the model.