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Subset Selection in Linear Regression using Sequentially Normalized Least Squares: Asymptotic Theory
Author(s) -
Määttä Jussi,
Schmidt Daniel F.,
Roos Teemu
Publication year - 2016
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12181
Subject(s) - mathematics , consistency (knowledge bases) , infinity , linear regression , asymptotic analysis , statistics , least squares function approximation , strong consistency , sample size determination , computation , selection (genetic algorithm) , zero (linguistics) , variance (accounting) , regression , mathematical analysis , discrete mathematics , algorithm , linguistics , philosophy , accounting , estimator , artificial intelligence , computer science , business
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.