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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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    1. Couillet, Romain & McKay, Matthew, 2014. "Large dimensional analysis and optimization of robust shrinkage covariance matrix estimators," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 99-120.
    2. Couillet, Romain & Pascal, Frédéric & Silverstein, Jack W., 2015. "The random matrix regime of Maronna’s M-estimator with elliptically distributed samples," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 56-78.
    3. Chikuse, Yasuko, 1990. "The matrix angular central Gaussian distribution," Journal of Multivariate Analysis, Elsevier, vol. 33(2), pages 265-274, May.
    4. Auderset, Claude & Mazza, Christian & Ruh, Ernst A., 2005. "Angular Gaussian and Cauchy estimation," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 180-197, March.
    5. Hendry, David F, 1986. "Econometric Modelling with Cointegrated Variables: An Overview," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 201-212, August.
    6. Strachan, R.W. & van Dijk, H.K., 2004. "Valuing structure, model uncertainty and model averaging in vector autoregressive processes," Econometric Institute Research Papers EI 2004-23, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    7. Strachan, Rodney W. & Inder, Brett, 2004. "Bayesian analysis of the error correction model," Journal of Econometrics, Elsevier, vol. 123(2), pages 307-325, December.
    8. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2019. "Priors for the Long Run," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 565-580, April.
    9. Gary Koop & Rodney Strachan & Herman van Dijk & Mattias Villani, 2004. "Bayesian Approaches to Cointegration," Discussion Papers in Economics 04/27, Division of Economics, School of Business, University of Leicester.
    10. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    11. Karlsson, Sune, 2013. "Forecasting with Bayesian Vector Autoregression," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 791-897, Elsevier.
    12. Cook, R. Dennis & Forzani, Liliana, 2009. "Likelihood-Based Sufficient Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 197-208.
    13. Villani, Mattias, 2005. "Bayesian Reference Analysis Of Cointegration," Econometric Theory, Cambridge University Press, vol. 21(2), pages 326-357, April.
    14. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
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