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Article overview
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Highly Efficient Estimators with High Breakdown Point for Linear Models with Structured Covariance Matrices | | Hendrik Paul Lopuhaä
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1 Aug 2022 | | Abstract: | We provide a unified approach to a method of estimation of the regression
parameter in balanced linear models with a structured covariance matrix that
combines a high breakdown point and bounded influence with high asymptotic
efficiency at models with multivariate normal errors. Of main interest are
linear mixed effects models, but our approach also includes several other
standard multivariate models, such as multiple regression, multivariate
regression, and multivariate location and scatter. We provide sufficient
conditions for the existence of the estimators and corresponding functionals,
establish asymptotic properties such as consistency and asymptotic normality,
and derive their robustness properties in terms of breakdown point and
influence function. All the results are obtained for general identifiable
covariance structures and are established under mild conditions on the
distribution of the observations, which goes far beyond models with
elliptically contoured densities. Some of our results are new and others are
more general than existing ones in the literature. In this way this manuscript
completes and improves results on high breakdown estimation with high
efficiency in a wide variety of multivariate models. | | Source: | arXiv, 2208.00715 | | Services: | Forum | Review | PDF | Favorites | |
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