A simultaneous estimation and variable selection rule

A new data-based method of estimation and variable selection in linear statistical models is proposed. This method is based on a generalized maximum entropy formalism, and makes use of both sample and non-sample information in determining a basis for coefficient shrinkage and extraneous variable identification. In contrast to tradition, shrinkage and variable selection are achieved on a coordinate-by-coordinate basis, and the procedure works well for both ill- and well-posed statistical models. Analytical asymptotic results are presented and sampling experiments are used as a basis for determining finite sample behavior and comparing the sampling performance of the new estimation rule with traditional competitors. Solution algorithms for the non-linear inversion problem that results are simple to implement.