TY - JOUR
T1 - Bootstrap for nonstandard cases
AU - Babu, Gutti Jogesh
N1 - Funding Information:
:~ Invited talk presented at "STATISTICS '91 CANADA", during May 23 25, 1991. 1 Research supproted in part by NSA Grant MDA904-90-H-1001.
PY - 1995/1
Y1 - 1995/1
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.
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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 -