{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T12:52:36Z","timestamp":1648990356820},"reference-count":39,"publisher":"Cambridge University Press (CUP)","issue":"03","license":[{"start":{"date-parts":[[2018,6,4]],"date-time":"2018-06-04T00:00:00Z","timestamp":1528070400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["www.cambridge.org"],"crossmark-restriction":true},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2019,6]]},"abstract":"<jats:p>Let <jats:italic>x<\/jats:italic> be a transformation of <jats:italic>y<\/jats:italic>, whose distribution is unknown. We derive an expansion formulating the expectations of <jats:italic>x<\/jats:italic> in terms of the expectations of <jats:italic>y<\/jats:italic>. Apart from the intrinsic interest in such a fundamental relation, our results can be applied to calculating E(<jats:italic>x<\/jats:italic>) by the low-order moments of a transformation which can be chosen to give a good approximation for E(<jats:italic>x<\/jats:italic>). 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.<\/jats:p>","DOI":"10.1017\/s026646661800021x","type":"journal-article","created":{"date-parts":[[2018,6,4]],"date-time":"2018-06-04T10:03:18Z","timestamp":1528106598000},"page":"630-652","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["LINK OF MOMENTS BEFORE AND AFTER TRANSFORMATIONS, WITH AN APPLICATION TO RESAMPLING FROM FAT-TAILED DISTRIBUTIONS"],"prefix":"10.1017","volume":"35","author":[{"given":"Karim 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