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Concentration inequalities for Gauss-Markov estimators

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  • Eaton, Morris L.

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.

Suggested Citation

  • Eaton, Morris L., 1988. "Concentration inequalities for Gauss-Markov estimators," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 119-138, April.
    • Handle: RePEc:eee:jmvana:v:25:y:1988:i:1:p:119-138
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    Cited by:

    1. Rustam Ibragimov, 2005. "Portfolio Diversification and Value At Risk Under Thick-Tailedness," Yale School of Management Working Papers amz2386, Yale School of Management, revised 01 Aug 2005.
    2. Rustam Ibragimov, 2004. "Shifting paradigms: on the robustness of economic models to heavy-tailedness assumptions," Econometric Society 2004 Latin American Meetings 105, Econometric Society.
    3. Rustam Ibragimov, 2005. "Portfolio Diversification and Value At Risk Under Thick-Tailedness," Yale School of Management Working Papers amz2386, Yale School of Management, revised 01 Aug 2005.

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