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 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.
| Original language | English (US) |
|---|---|
| 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
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Bootstrap for nonstandard cases. / Babu, G. Jogesh.
In: Journal of Statistical Planning and Inference, Vol. 43, No. 1-2, 01.01.1995, p. 197-203.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 -