The Expected Sample Variance of Uncorrelated Random Variables with a Common Mean and Some Applications in Unbalanced Random Effects Models

File
2005_VardemanSB_ExpectedSampleVariance.pdf (292.66 KB)
0-2005_Journal_of_Statistics_Education_permission.pdf (263.51 KB)
Supplemental Files
0-2005_Journal_of_Statistics_Education_permission.pdf (263.51 KB)
Date
2005-03-01
Authors
Vardeman, Stephen
Wendelberger, Joanne
Vardeman, Stephen
Journal Title
Journal ISSN
Volume Title
Publisher
Altmetrics
Authors
Research Projects
Organizational Units
Statistics
Organizational Unit
Journal Issue
Series
Abstract

There is a little-known but very simple generalization of the standard result that for uncorrelated random variables with common mean µ and variance 2 σ , the expected value of the sample variance is 2 σ . The generalization justifies the use of the usual standard error of the sample mean in possibly heteroscedastic situations, and motivates elementary estimators in even unbalanced linear random effects models. The latter both provides nontrivial examples and exercises concerning method-of-moments estimation, and also helps "demystify" the whole matter of variance component estimation. This is illustrated in general for the simple one-way context and for a specific unbalanced two-factor hierarchical data structure.

Description

This article is from Journal of Statistics Education 13 (2005): www.amstat.org/publications/jse/v13n1/vardeman.html

Keywords
Heteroscedastic, Method of moments, One-way model, Two-factor hierarchical model, Standard error of the mean, Variance component
Citation
DOI
Collections