Resampling Fewer Than n Observations: Gains, Losses, and Remedies for Losses

Abstract

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.

Statistical foundations for assessing the difference between the classical and weighted-Gini betas

“…This prompts us to think of another method for estimating the critical values, and bootstrap is an attractive option (e.g., Chernick and LaBudde, 2011;and references therein). It is well known, however, that bootstrap may not always work (e.g., Athreya, 1987;Bickel et al, 1997;Hall, 1992;Mammen, 1992), but when the underlying asymptotic normality is established (e.g., Hall, 1992;Mammen, 1992), the bootstrap does work. This reveals the value of Theorem 2.3 even when its direct use for producing statistical inference has been circumvented by bootstrap, either naive or more advanced, like for example "m out of n" as in Bickel et al (1997); see also Helmers (2007, 2011), and references therein.…”

A general bootstrap performance diagnostic

“…A number of avenues of potential future work remain. For example, it would be interesting to apply our diagnostic procedure to other estimator quality assessment methods [4,17,13] and to devise extensions of the diagnostic which are suitable for variants of the bootstrap designed to handle non-i.i.d. data [9,12,14,16,18].…”

“…Indeed, like any inferential procedure, despite its excellent theoretical properties and frequently excellent empirical performance, the bootstrap is not infallible. For example, it may fail to be consistent in particular settings (i.e., for particular pairs of estimators and data generating distributions) [19,4]. While theoretical conditions yielding consistency are well known, they can be non-trivial to verify analytically and provide little useful guidance in the absence of manual analysis.…”

International market links and volatility transmission

“…To circumvent the above issues, we resort to a variation of the standard moon bootstrap by Bretagnolle (1983) and Bickel et al (1997). We sample T out of T daily realized measures by blocks (rather than individually) so as to cope with time-series dependence.…”