• français
    • English
  • English 
    • français
    • English
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
BIRD Home

Browse

This CollectionBy Issue DateAuthorsTitlesSubjectsJournals BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesSubjectsJournals

My Account

Login

Statistics

View Usage Statistics

A few properties of sample variance

Thumbnail
Date
2018
Publisher city
Paris
Publisher
Preprint Lamsade
Collection title
Preprint Lamsade
Link to item file
https://hal.archives-ouvertes.fr/hal-02012458
Dewey
Probabilités et mathématiques appliquées
Sujet
independence between sample mean and variance; sample variance; variance of sample variance
URI
https://basepub.dauphine.fr/handle/123456789/18911
Collections
  • LAMSADE : Publications
Metadata
Show full item record
Author
Benhamou, Eric
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Type
Document de travail / Working paper
Item number of pages
15
Abstract (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

  • Accueil Bibliothèque
  • Site de l'Université Paris-Dauphine
  • Contact
SCD Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16

 Content on this site is licensed under a Creative Commons 2.0 France (CC BY-NC-ND 2.0) license.