Exploring the Limits

Lange, Ulrich T.; Goldhammer, Klaus

doi:10.1007/978-3-642-60746-2

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“…In most cases, each resample from step 2 is of size n, but there are known situations where a different choice is desirable, primarily related to inferences for extremes where the random variables may follow a heavy-tail distribution; that is, the probability of observing increasingly high (or low) values decays polynomially. In this case, resamples of size m , n where m/n / 0 as m / ' and n / '; e.g., m 5 ffiffiffi n p (Bickel and Freedman 1981;Arcones andGiné 1989, 1991;Athreya 1987a,b;Giné and Zinn 1989;Knight 1989;Hall 1990;Kinateder 1992;LePage 1992;Deheuvels et al 1993;Fukuchi 1994;Bickel et al 1997;Feigin and Resnick 1997;Lee 1999;Shao and Dongsheng 1995;Resnick 2007).…”

Section: ) Resample Sizesmentioning

confidence: 99%

Bootstrap Methods for Statistical Inference. Part I: Comparative Forecast Verification for Continuous Variables

Gilleland

2020

Journal of Atmospheric and Oceanic Technology

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When making statistical inferences, bootstrap resampling methods are often appealing because of less stringent assumptions about the distribution of the statistic(s) of interest. However, the procedures are not free of assumptions. This paper addresses a specific situation that occurs frequently in atmospheric sciences where the standard bootstrap is not appropriate; comparative forecast verification of continuous variables. In this setting, the question to be answered concerns which of twoweather or climate models is better in the sense of some type of average deviation from observations. The series to be compared are generally strongly dependent, which invalidates the most basic bootstrap technique. This paper also introduces new bootstrap code from the R package distillery that facilitates easy implementation of appropriate methods for paired-difference-of-means bootstrap procedures for dependent data.

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