Related papers: Improved Covariance Matrix Estimator using Shrinka…

Shrinkage can effectively improve the condition number and accuracy of covariance matrix estimation, especially for low-sample-support applications with the number of training samples smaller than the dimensionality. This paper investigates…

We introduce a covariance matrix estimator that both takes into account the heteroskedasticity of financial returns (by using an exponentially weighted moving average) and reduces the effective dimensionality of the estimation (and hence…

The estimation of covariance matrices of multiple classes with limited training data is a difficult problem. The sample covariance matrix (SCM) is known to perform poorly when the number of variables is large compared to the available…

The kernel trick concept, formulated as an inner product in a feature space, facilitates powerful extensions to many well-known algorithms. While the kernel matrix involves inner products in the feature space, the sample covariance matrix…

The global minimum-variance portfolio is a typical choice for investors because of its simplicity and broad applicability. Although it requires only one input, namely the covariance matrix of asset returns, estimating the optimal solution…

Covariance estimation for matrix-valued data has received an increasing interest in applications. Unlike previous works that rely heavily on matrix normal distribution assumption and the requirement of fixed matrix size, we propose a class…

The comovement phenomenon in financial markets creates decision scenarios with positively correlated asset returns. This paper addresses covariance matrix estimation under such conditions, motivated by observations of significant positive…

The state-of-the-art methods for estimating high-dimensional covariance matrices all shrink the eigenvalues of the sample covariance matrix towards a data-insensitive shrinkage target. The underlying shrinkage transformation is either…

This article studies two regularized robust estimators of scatter matrices proposed (and proved to be well defined) in parallel in (Chen et al., 2011) and (Pascal et al., 2013), based on Tyler's robust M-estimator (Tyler, 1987) and on…

Shrinkage estimators of covariance are an important tool in modern applied and theoretical statistics. They play a key role in regularized estimation problems, such as ridge regression (aka Tykhonov regularization), regularized discriminant…

Covariance matrices estimated from short, noisy, and non-Gaussian financial time series are notoriously unstable. Empirical evidence suggests that such covariance structures often exhibit power-law scaling, reflecting complex, hierarchical…

This chapter reviews methods for linear shrinkage of the sample covariance matrix (SCM) and matrices (SCM-s) under elliptical distributions in single and multiple populations settings, respectively. In the single sample setting a popular…

We develop a method for estimating well-conditioned and sparse covariance and inverse covariance matrices from a sample of vectors drawn from a sub-gaussian distribution in high dimensional setting. The proposed estimators are obtained by…

Portfolio managers faced with limited sample sizes must use factor models to estimate the covariance matrix of a high-dimensional returns vector. For the simplest one-factor market model, success rests on the quality of the estimated…

We study the allocation of synthetic portfolios under hierarchical nested, one-factor, and diagonal structures of the population covariance matrix in a high-dimensional scenario. The noise reduction approaches for the sample realizations…

Covariance matrix estimation and principal component analysis (PCA) are two cornerstones of multivariate analysis. Classic textbook solutions perform poorly when the dimension of the data is of a magnitude similar to the sample size, or…

We present a comparison between various algorithms of inference of covariance and precision matrices in small datasets of real vectors, of the typical length and dimension of human brain activity time series retrieved by functional Magnetic…

When shrinking a covariance matrix towards (a multiple) of the identity matrix, the trace of the covariance matrix arises naturally as the optimal scaling factor for the identity target. The trace also appears in other context, for example…

This paper considers the regularized estimation of covariance matrices (CM) of high-dimensional (compound) Gaussian data for minimum variance distortionless response (MVDR) beamforming. Linear shrinkage is applied to improve the accuracy…

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…