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High Dimensional Covariance Estimation: Avoiding the ‘Curse of Dimensionality’

In: Proceedings of the First US/Japan Conference on the Frontiers of Statistical Modeling: An Informational Approach

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  • Robert M. Pruzek

    (State University of New York at Albany, Departments of Educational Psychology & Statistics and Biometry and Statistics)

Abstract

A central problem in standard parametric applications of multivariate analysis is covariance estimation, particularly relatively stable and robust estimation of covariance matrices as well as their inverses to support standard inferential decisions and conc1usions. Despite the fundamental role played by covariance estimation in many common statistical applications, relatively few resources appear to have gone into its study and improvement compared to work expended on allied statistics. This is difficult to understand in view of the complexities and ambiguities in the theory that supports standard covariance estimation, particularly when p, the number of observed variables, is a substantial fraction of n, the sample size.

Suggested Citation

  • Robert M. Pruzek, 1994. "High Dimensional Covariance Estimation: Avoiding the ‘Curse of Dimensionality’," Springer Books, in: Hamparsum Bozdogan & Stanley L. Sclove & Arjun K. Gupta & D. Haughton & G. Kitagawa & T. Ozaki & K. (ed.), Proceedings of the First US/Japan Conference on the Frontiers of Statistical Modeling: An Informational Approach, chapter 8, pages 233-253, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-0800-3_9
    DOI: 10.1007/978-94-011-0800-3_9
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