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On the Effect of Unbalancedness and Heteroscedasticity on the ANOVA Estimator of Group Variance Component in One‐Way Random Model
Author(s) -
Singh B.
Publication year - 1992
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710340109
Subject(s) - heteroscedasticity , mathematics , statistics , estimator , analysis of variance , variance (accounting) , one way analysis of variance , mean squared error , econometrics , bias of an estimator , minimum variance unbiased estimator , economics , accounting
The expression for r th cumulant of ANOVA estimator of group variance component is derived in the One‐way unbalanced random model under heteroscedasticity. The expression is used to study the effect of unbalancedness and heteroscedasticity on the mean and variance of the estimator, numerically. The computed results reveal that the unbalancedness and heteroscedasticity have a combined effect on the mean and variance of the estimator. For certain situations of unequal group sizes and error variances, the mean and variance of the estimator are increased and for certain other situations the values are decreased.