### 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) |
---|---|

Pages (from-to) | 497-515 |

Number of pages | 19 |

Journal | Statistica Sinica |

Volume | 10 |

Issue number | 2 |

State | Published - Apr 1 2000 |

### Fingerprint

### Keywords

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

### Cite this

*Statistica Sinica*,

*10*(2), 497-515.

**Variance estimation in high dimensional regression models.** / Chatterjee, Snigdhansu; Bose, Arup.

Research output: Contribution to journal › Article

*Statistica Sinica*, vol. 10, no. 2, pp. 497-515.

}

TY - JOUR

T1 - Variance estimation in high dimensional regression models

AU - Chatterjee, Snigdhansu

AU - Bose, Arup

PY - 2000/4/1

Y1 - 2000/4/1

N2 - 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).

AB - 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).

KW - Bootstrap

KW - Dimension asymptotics

KW - Jackknife

KW - Many parameter regression

KW - Variance estimation

UR - http://www.scopus.com/inward/record.url?scp=0034377904&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034377904&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0034377904

VL - 10

SP - 497

EP - 515

JO - Statistica Sinica

JF - Statistica Sinica

SN - 1017-0405

IS - 2

ER -