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Robust estimation of variance components
Author(s) -
Gervini Daniel,
Yohai Victor J.
Publication year - 1998
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315766
Subject(s) - statistics , mathematics , estimator , variance based sensitivity analysis , variance (accounting) , outlier , monte carlo method , robust regression , generalized least squares , least squares function approximation , one way analysis of variance , variance components , linear regression , variance function , analysis of variance , accounting , business
New robust estimates for variance components are introduced. Two simple models are considered: the balanced one‐way classification model with a random factor and the balanced mixed model with one random factor and one fixed factor. However, the method of estimation proposed can be extended to more complex models. The new method of estimation we propose is based on the relationship between the variance components and the coefficients of the least‐mean‐squared‐error predictor between two observations of the same group. This relationship enables us to transform the problem of estimating the variance components into the problem of estimating the coefficients of a simple linear regression model. The variance‐component estimators derived from the least‐squares regression estimates are shown to coincide with the maximum‐likelihood estimates. Robust estimates of the variance components can be obtained by replacing the least‐squares estimates by robust regression estimates. In particular, a Monte Carlo study shows that for outlier‐contaminated normal samples, the estimates of variance components derived from GM regression estimates and the derived test outperform other robust procedures.