he covariance matrix of asset returns is important for a wide range of individuals.1 Academics use estimates of the covariance matrix to test asset-pricing theories. Portfolio managers use the covariance matrix in designing tracking strategies where the return on their portfolio is designed to closely follow the return on a benchmark portfolio. Risk managers use the matrix to construct measures...

A computationally e cient method for structured covariance matrix estimation is presented. The proposed method provides an Asymptotic (for large samples) Maximum Likelihood estimate of a structured covariance matrix and is referred to as AML. A closed-form formula for estimating Hermitian Toeplitz covariance matrices is derived which makes AML computationally much simpler than most existing Her...

In classifying samples by Gaussian clas-siier, the covariance matrix estimated with a small number sample set becomes unstable, which leads to degrading the classiication accuracy. In this paper , we discuss the covariance matrix estimation problem for small number samples with high dimension setting based on Kullback-Leibler Information Measure. A new covariance matrix estimator is developed, ...

Structural equation modeling [1] has been used in a variety of research applications in the social and behavioral sciences. A broad-spectrum aim of SEM can be expressed as testing the hypothesis that the population-level covariance matrix for a set of measured indicator variables is equal to the model-implied covariance matrix based on the hypothesized factor model. And, this relationship can b...

In many practical applications second order moments are used for estimation of power spectrum. This can be cast as an inverse problem where we seek a spectrum consistent with a given state-covariance matrix. Such a solution exists if and only if the covariance matrix is positive and belong to a low dimensional subspace. The sample covariance estimate of such a matrix will typically fall outside...

The linear minimum mean-squared error (MMSE) detector for direct-sequence code-division multiple-access (DSCDMA) systems relies on the inverse of the covariance matrix of the received signal. In multiuser environments, when few samples are available for the covariance estimation, the matrix illconditioning may produce large performance degradation. In order to cope with this effect, we propose ...

Many applied problems require a covariance matrix estimator that is not only invertible, but also well-conditioned (that is, inverting it does not amplify estimation error). For largedimensional covariance matrices, the usual estimator—the sample covariance matrix—is typically not well-conditioned and may not even be invertible. This paper introduces an estimator that is both well-conditioned a...

Cap and swaption prices contain information on interest rate volatilities and correlations. In this paper, we examine whether this information in cap and swaption prices is consistent with realized movements of the interest rate term structure. To extract an option-implied interest rate covariance matrix from cap and swaption prices, we use Libor market models or discrete-tenor string models as...

Estimating the eigenvalues of a population covariance matrix from a sample covariance matrix is a problem of fundamental importance in multivariate statistics; the eigenvalues of covariance matrices play a key role in many widely techniques, in particular in Principal Component Analysis (PCA). In many modern data analysis problems, statisticians are faced with large datasets where the sample si...

Model evaluation in covariance structure analysis is critical before the results can be trusted. Due to finite sample sizes and unknown distributions of real data, existing conclusions regarding a particular statistic may not be applicable in practice. The bootstrap procedure automatically takes care of the unknown distribution and, for a given sample size, also provides more accurate results t...