Abadir, Karim Maher and Cornea-Madeira, Adriana orcid.org/0000-0002-0889-7145 (2019) Link of moments before and after transformations, with an application to resampling from fat-tailed distributions. Econometric Theory. pp. 630-652. ISSN 0266-4666
Abstract
Let x be a transformation of y, whose distribution is unknown. We derive an expansion formulating the expectations of x in terms of the expectations of y. Apart from the intrinsic interest in such a fundamental relation, our results can be applied to calculating E(x) by the low-order moments of a transformation which can be chosen to give a good approximation for E(x). To do so, we generalize the approach of bounding the terms in expansions of characteristic functions, and use our result to derive an explicit and accurate bound for the remainder when a finite number of terms is taken. We illustrate one of the implications of our method by providing accurate naive bootstrap confidence intervals for the mean of any fat-tailed distribution with an infinite variance, in which case currently available bootstrap methods are asymptotically invalid or unreliable in finite samples.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Cambridge University Press 2018. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details |
Dates: |
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Institution: | The University of York |
Academic Units: | The University of York > Faculty of Social Sciences (York) > The York Management School |
Depositing User: | Pure (York) |
Date Deposited: | 17 May 2018 14:50 |
Last Modified: | 16 Oct 2024 14:44 |
Published Version: | https://doi.org/10.1017/S026646661800021X |
Status: | Published |
Refereed: | Yes |
Identification Number: | 10.1017/S026646661800021X |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:131025 |
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