### Abstract

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 p^{2}/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 language | English (US) |
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Pages (from-to) | 497-515 |

Number of pages | 19 |

Journal | Statistica Sinica |

Volume | 10 |

Issue number | 2 |

State | Published - Apr 1 2000 |

### Keywords

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

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## Cite this

Chatterjee, S., & Bose, A. (2000). Variance estimation in high dimensional regression models.

*Statistica Sinica*,*10*(2), 497-515.