A law of the single logarithm for weighted sums of arrays applied to bootstrap model selection in regression

Pierre Lafaye de Micheaux and Christian Léger

Statistics & Probability Letters, 2012, vol. 82, issue 5, 965-971

Abstract: We generalize a law of the single logarithm obtained by Qi (1994) and Li et al. (1995) to the case of weighted sums of triangular arrays of random variables. We apply this result to bootstrapping the all-subsets model selection problem in regression, where we show that the popular Bayesian Information Criterion of Schwarz (1978) is no longer asymptotically consistent.

Keywords: BIC; Linear regression; Variable selection; Rowwise independent; Triangular arrays (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spl.2012.01.018

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