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Consistency and asymptotic normality of M-estimates of scatter on Grassmann manifolds

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  • Ciobotaru, Corina
  • Mazza, Christian

Abstract

This work proposes a study of M-estimates of scatter for matrix angular central Gaussian distributions on Grassmann manifold G(m,r) of all vector subspaces of dimension r of Rm. Such distributions are associated to random subspaces generated by r i.i.d. multivariate centred normal random vectors, and are of interest in Bayesian model selection for cointegration. We provide a careful study of the existence and the unicity of such M-estimators using geometrical arguments, and then study their consistency and asymptotic normality.

Suggested Citation

  • Ciobotaru, Corina & Mazza, Christian, 2022. "Consistency and asymptotic normality of M-estimates of scatter on Grassmann manifolds," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:jmvana:v:190:y:2022:i:c:s0047259x2200032x
    DOI: 10.1016/j.jmva.2022.104998
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    References listed on IDEAS

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