  We mainly study the M-estimation method for the high-dimensional linear
regression model, and discuss the properties of M-estimator when the penalty
term is the local linear approximation. In fact, M-estimation method is a
framework, which covers the methods of the least absolute deviation, the
quantile regression, least squares regression and Huber regression. We show
that the proposed estimator possesses the good properties by applying certain
assumptions. In the part of numerical simulation, we select the appropriate
algorithm to show the good robustness of this method
