Lq penalized regression

For linear regression problems, the Ordinary Least Squares (OLS) model produces unbi- ased estimates but can have large variances if the design matrix X is close to collinear, and the estimator is not unique if X is less than full rank. To remedy these problems, penal- ized regression methods such as Ridge, Lasso and Enet have been developed, which have improved OLS in some respects, but failed in others. We study Lq Bridge regressor with q > 0 using local quadratic approximation. By letting the q be estimated from the given data, the method extends its practicality. We thoroughly compare all kinds of regression methods under various simulation settings and a real example. Our goal is to assess the per- formance of Lq regressor and to examine the behavior of tuning parameters. The simulation result shows that Lq regressor is very robust as it performs well in all different cases.