Concentration inequalities for Gauss-Markov estimators

Morris L. Eaton

Journal of Multivariate Analysis, 1988, vol. 25, issue 1, 119-138

Abstract: Let M be the regression subspace and [gamma] the set of possible covariances for a random vector Y. The linear model determined by M and [gamma] is regular if the identity is in [gamma] and if [Sigma](M)[subset, double equals]M for all [Sigma][set membership, variant][gamma]. For such models, concentration inequalities are given for the Gauss-Markov estimator of the mean vector under various distributional and invariance assumptions on the error vector. Also, invariance is used to establish monotonicity results relative to a natural group induced partial ordering.

Keywords: Gauss; Markov; estimators; concentration; inequalities; elliptical; densities; log; concave; densities; majorization; group; induced; orderings; reflection; groups (search for similar items in EconPapers)
Date: 1988
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Citations: View citations in EconPapers (3)

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