Abstract:We discuss a number of resampling schemes in which m = o(n) observations are resampled. We review nonparametric bootstrap failure and give results old and new on how the m out of n with replacement and without replacement bootstraps work. We extend work of Bickel and Yahav (1988) to show that m out of n bootstraps can be made second order correct , if the usual nonparametric bootstrap is correct and study how these extrapolation techniques work when the nonparametric bootstrap does not.
We propose a test for the null hypothesis that two sets of vectors are drawn from the same multidimensional probability distribution. The application to delay vector distributions provides a test for the null hypothesis that two time series have been generated by the same mechanism.PACS number(s): 02.50. -r, 05.40. +j, 05.45. +b
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