Variance estimation in high dimensional regression models

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We treat the problem of variance estimation of the least squares estimate of the parameter in high dimensional linear regression models by using the Uncorrelated Weights Bootstrap (UBS). We find a representation of the UBS dispersion matrix and show that the bootstrap estimator is consistent if p2/n → 0 where p is the dimension of the parameter and n is the sample size. For fixed dimension we show that the UBS belongs to the R-class as defined in Liu and Singh (1992).

Original languageEnglish (US)
Pages (from-to)497-515
Number of pages19
JournalStatistica Sinica
Issue number2
StatePublished - Apr 1 2000


  • Bootstrap
  • Dimension asymptotics
  • Jackknife
  • Many parameter regression
  • Variance estimation


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