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.
All Science Journal Classification (ASJC) codes
- Statistics, Probability and Uncertainty
- Applied Mathematics
- Statistics and Probability