dc.contributor.author Benhamou, Eric dc.date.accessioned 2019-05-15T10:42:13Z dc.date.available 2019-05-15T10:42:13Z dc.date.issued 2018 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/18911 dc.language.iso en en dc.subject independence between sample mean and variance en dc.subject sample variance en dc.subject variance of sample variance en dc.subject.ddc 519 en dc.title A few properties of sample variance en dc.type Document de travail / Working paper dc.description.abstracten A basic result is that the sample variance for i.i.d. observations is an unbiased esti-mator of the variance of the underlying distribution (see for instance Casella and Berger(2002)). But what happens if the observations are neither independent nor identically distributed. What can we say? Can we in particular compute explicitly the firsttwo moments of the sample mean and hence generalize formulae provided in Tukey(1957a), Tukey (1957b) for the first two moments of the sample variance? We also know that the sample mean and variance are independent if they are computed onan i.i.d. normal distribution. This is one of the underlying assumption to derive theStudent distribution Student alias W. S. Gosset (1908). But does this result hold forany other underlying distribution? Can we still have independent sample mean andvariance if the distribution is not normal? This paper precisely answers these questions and extends previous work of Cho, Cho, and Eltinge (2004). We are able to derive ageneral formula for the first two moments and variance of the sample variance under nospecific assumptions. We also provide a faster proof of a seminal result of Lukacs (1942)by using the log characteristic function of the unbiased sample variance estimator. en dc.publisher.name Preprint Lamsade en dc.publisher.city Paris en dc.identifier.citationpages 15 en dc.relation.ispartofseriestitle Preprint Lamsade en dc.identifier.urlsite https://hal.archives-ouvertes.fr/hal-02012458 en dc.subject.ddclabel Probabilités et mathématiques appliquées en dc.description.ssrncandidate non en dc.description.halcandidate non en dc.description.readership recherche en dc.description.audience International en dc.date.updated 2019-04-30T12:04:45Z hal.person.labIds 989
﻿

## Files in this item

FilesSizeFormatView

There are no files associated with this item.