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

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  • Lafaye de Micheaux, Pierre
  • Léger, Christian

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.

Suggested Citation

  • Lafaye de Micheaux, Pierre & Léger, Christian, 2012. "A law of the single logarithm for weighted sums of arrays applied to bootstrap model selection in regression," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 965-971.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:5:p:965-971
    DOI: 10.1016/j.spl.2012.01.018
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    References listed on IDEAS

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    1. Li, Deli & Qi, Yongcheng & Rosalsky, Andrew, 2009. "Iterated logarithm type behavior for weighted sums of i.i.d. random variables," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 643-651, March.
    2. Sung, Soo Hak, 2009. "A law of the single logarithm for weighted sums of i.i.d. random elements," Statistics & Probability Letters, Elsevier, vol. 79(10), pages 1351-1357, May.
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