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Dimension from covariance matrices

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2017
We describe a method to estimate embedding dimension from a time series. This method includes an estimate of the probability that the dimension estimate is valid. Such validity estimates are not common in algorithms for calculating the properties of dynamical systems.
T. L. Carroll, J. M. Byers
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Estimating complex covariance matrices

Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, 2004., 2005
The problem of estimating complex covariance matrices is considered. The objective is to obtain a well behaving estimator that circumvents the weaknesses of the standard sample covariance and regularized estimators. To this end, we use a variational technique that previously has been successfully applied in the real data case.
L. Svensson, M. Lundberg
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Eigen-Adjusted Covariance Matrices

SSRN Electronic Journal, 2011
The Markowitz mean-variance framework is the foundation of modern portfolio theory. One problem with this approach, however, is how sample covariance matrices tend to underestimate risk. Since the biases of optimized portfolios are closely related to eigenfactor portfolios, we present a methodology for estimating biases in eigenfactor volatilities, and
Jose Menchero, Jun Wang, D.J. Orr
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Graphical Comparison of Covariance Matrices

Australian Journal of Statistics, 1981
SummaryProcedures for comparing within‐group covariance matrices are developed, based on separate analyses of the variances and of the correlations. The variances and the correlations are represented as two two‐way tables, with the columns representing groups. Graphical procedures based on comparisons of linear regressions are presented, by considering
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Extremal Covariance Matrices

2018
The tail dependence coefficient (TDC) is a natural tool to describe extremal dependence. Estimation of the tail dependence coefficient can be performed via empirical process theory. In case of extremal independence, the limit degenerates and hence one cannot construct a test for extremal independence.
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Covariance Function Matrices

1995
It is actually difficult to characterize directly a covariance function matrix. This becomes easy in the spectral domain on the basis of Cramer’s generalization of the Bochner theorem, which is presented in this chapter. We consider complex covariance functions.
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Semi-tied covariance matrices

Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181), 2002
A standard problem in many classification tasks is how to model feature vectors whose elements are highly correlated. If multi-variate Gaussian distributions are used to model the data then they must have full covariance matrices to accurately do so. This requires a large number of parameters per distribution which restricts the number of distributions
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Three‐mode analysis of multimode covariance matrices

British Journal of Mathematical and Statistical Psychology, 2003
Multimode covariance matrices, such as multitrait‐multimethod matrices, contain the covariances of subject scores on variables for different occasions or conditions. This paper presents a comparison of three‐mode component analysis and three‐mode factor analysis applied to such covariance matrices.
Kroonenberg, P.M., Oort, F.J.
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Testing Pattern Hypotheses for Covariance Matrices

Psychometrika, 1974
Maximum likelihood estimates of the free parameters, and an asymptotic likelihood-ratio test, are given for the hypothesis that one or more elements of a covariance matrix are zero, and/or that two or more of its elements are equal. The theory applies immediately to a transformation of the covariance matrix by a known nonsingular matrix.
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Spectral Properties of Sample Covariance Matrices

Theory of Probability & Its Applications, 1996
Summary: The expectation value of the resolvents of sample covariance matrices and the variance of their matrix elements are investigated. It is assumed only that variables have zero expectation values and the maximal fourth moment of variables exists. The principal spectral equations obtained earlier only in the form of limit formulas are derived with
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