A few properties of sample variance
Date
2018Publisher city
ParisPublisher
Preprint LamsadeCollection title
Preprint LamsadeLink to item file
https://hal.archives-ouvertes.fr/hal-02012458Dewey
Probabilités et mathématiques appliquéesSujet
independence between sample mean and variance; sample variance; variance of sample varianceCollections
Metadata
Show full item recordAuthor
Benhamou, Eric
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Type
Item number of pages
15Abstract (EN)
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.Related items
Showing items related by title, author, creator and subject.
-
Calibration of local volatility using the local and implied instantaneous variance
Turinici, Gabriel (2009) Article accepté pour publication ou publié -
Impact de l'intervalle d’échantillonnage sur les tests d’efficience : application au marché français des actions
Alexandre, Hervé; Ertur, Kamil Cem (1994-12) Article accepté pour publication ou publié -
Retraite et risque financier
Pradat, Yannick (2017-07-04) Thèse