Abstract
Selection from a finite population is used in several procedures in statistics, among others in bootstrap and permutation methods. In this paper we give a survey of some recent results for selection in “nonstandard” situations, i.e. in cases when the negligibility condition of classical central limit theory is not satisfied. These results enable us to describe the asymptotic properties of bootstrap and permutation statistics in case of infinite variances, when the limiting processes contain random coefficients. We will also show that random limit distributions can be avoided by a suitable trimming of the sample, making bootstrap and permutation methods applicable for statistical inference under infinite variances.
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Berkes, I., Horváth, L., Schauer, J. (2010). Permutation and bootstrap statistics under infinite variance. In: Doukhan, P., Lang, G., Surgailis, D., Teyssière, G. (eds) Dependence in Probability and Statistics. Lecture Notes in Statistics(), vol 200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14104-1_1
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DOI: https://doi.org/10.1007/978-3-642-14104-1_1
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