Subset Selection in Linear Regression using Sequentially Normalized Least Squares: Asymptotic Theory |
| |
Authors: | Jussi Määttä Daniel F. Schmidt Teemu Roos |
| |
Affiliation: | 1. Helsinki Institute for Information Technology HIIT, Department of Computer ScienceUniversity of Helsinki;2. Centre for Epidemiology and BiostatisticsThe University of Melbourne |
| |
Abstract: | This article examines the recently proposed sequentially normalized least squares criterion for the linear regression subset selection problem. A simplified formula for computation of the criterion is presented, and an expression for its asymptotic form is derived without the assumption of normally distributed errors. Asymptotic consistency is proved in two senses: (i) in the usual sense, where the sample size tends to infinity, and (ii) in a non‐standard sense, where the sample size is fixed and the noise variance tends to zero. |
| |
Keywords: | asymptotics consistency linear regression minimum description length principle subset selection |
|