Subset selection in linear regression using sequentially normalized least squares: asymptotic theory

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.