### Abstract

Scale invariant statistics like Student's t, involving mean absolute deviations instead of standard deviations, and statistics which are distributed asymptotically like linear combinations of chi-squares or F-statistics are considered. Bootstrap procedures in estimating their distributions are described. The error in the bootstrap approximation of the sampling distribution, in the latter type, is of the order O_{p}(n^{- 3 1}). It is demonstrated that the error term cannot be improved. In such cases Bartlett correction is preferable, which is known to give an approximation with an error term of the order O(n^{-2}). Bootstrap procedures for errors-in-variables regression coefficients are also described. In all the cases mentioned above, the Edgeworth expansions of multivariate means, which do not satisfy standard regularity assumptions, play an important role.

Original language | English (US) |
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Pages (from-to) | 197-203 |

Number of pages | 7 |

Journal | Journal of Statistical Planning and Inference |

Volume | 43 |

Issue number | 1-2 |

DOIs | |

State | Published - Jan 1 1995 |

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### All Science Journal Classification (ASJC) codes

- Statistics, Probability and Uncertainty
- Applied Mathematics
- Statistics and Probability

### Cite this

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*Journal of Statistical Planning and Inference*, vol. 43, no. 1-2, pp. 197-203. https://doi.org/10.1016/0378-3758(94)00019-R

**Bootstrap for nonstandard cases.** / Babu, G. Jogesh.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Bootstrap for nonstandard cases

AU - Babu, G. Jogesh

PY - 1995/1/1

Y1 - 1995/1/1

N2 - Scale invariant statistics like Student's t, involving mean absolute deviations instead of standard deviations, and statistics which are distributed asymptotically like linear combinations of chi-squares or F-statistics are considered. Bootstrap procedures in estimating their distributions are described. The error in the bootstrap approximation of the sampling distribution, in the latter type, is of the order Op(n- 3 1). It is demonstrated that the error term cannot be improved. In such cases Bartlett correction is preferable, which is known to give an approximation with an error term of the order O(n-2). Bootstrap procedures for errors-in-variables regression coefficients are also described. In all the cases mentioned above, the Edgeworth expansions of multivariate means, which do not satisfy standard regularity assumptions, play an important role.

AB - Scale invariant statistics like Student's t, involving mean absolute deviations instead of standard deviations, and statistics which are distributed asymptotically like linear combinations of chi-squares or F-statistics are considered. Bootstrap procedures in estimating their distributions are described. The error in the bootstrap approximation of the sampling distribution, in the latter type, is of the order Op(n- 3 1). It is demonstrated that the error term cannot be improved. In such cases Bartlett correction is preferable, which is known to give an approximation with an error term of the order O(n-2). Bootstrap procedures for errors-in-variables regression coefficients are also described. In all the cases mentioned above, the Edgeworth expansions of multivariate means, which do not satisfy standard regularity assumptions, play an important role.

UR - http://www.scopus.com/inward/record.url?scp=58149322416&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58149322416&partnerID=8YFLogxK

U2 - 10.1016/0378-3758(94)00019-R

DO - 10.1016/0378-3758(94)00019-R

M3 - Article

AN - SCOPUS:58149322416

VL - 43

SP - 197

EP - 203

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

IS - 1-2

ER -