Related papers: Cleaning large-dimensional covariance matrices for…
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…
We study general singular value shrinkage estimators in high-dimensional regression and classification, when the number of features and the sample size both grow proportionally to infinity. We allow models with general covariance matrices…
The traditional class of elliptical distributions is extended to allow for asymmetries. A completely robust dispersion matrix estimator (the `spectral estimator') for the new class of `generalized elliptical distributions' is presented. It…
In this paper, we study the problem of high-dimensional approximately low-rank covariance matrix estimation with missing observations. We propose a simple procedure computationally tractable in high-dimension and that does not require…
Linear shrinkage estimators of a covariance matrix --- defined by a weighted average of the sample covariance matrix and a pre-specified shrinkage target matrix --- are popular when analysing high-throughput molecular data. However, their…
We study the estimation of the high-dimensional covariance matrix andits eigenvalues under dynamic volatility models. Data under such modelshave nonlinear dependency both cross-sectionally and temporally. We firstinvestigate the empirical…
This paper studies the covariance matrix estimation for high-dimensional time series within a new framework that combines low-rank factor and latent variable-specific cluster structures. The popular methods based on assuming the sparse…
This paper studies the estimation of a large covariance matrix. We introduce a novel procedure called ChoSelect based on the Cholesky factor of the inverse covariance. This method uses a dimension reduction strategy by selecting the pattern…
We study high-dimensional covariance/precision matrix estimation under the assumption that the covariance/precision matrix can be decomposed into a low-rank component L and a diagonal component D. The rank of L can either be chosen to be…
Fitting high-dimensional data involves a delicate tradeoff between faithful representation and the use of sparse models. Too often, sparsity assumptions on the fitted model are too restrictive to provide a faithful representation of the…
Sparse covariance matrices play crucial roles by encoding the interdependencies between variables in numerous fields such as genetics and neuroscience. Despite substantial studies on sparse covariance matrices, existing methods face several…
We introduce an estimation method of covariance matrices in a high-dimensional setting, i.e., when the dimension of the matrix, , is larger than the sample size . Specifically, we propose an orthogonally equivariant estimator. The…
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…
This paper considers the problem of estimating a high-dimensional (HD) covariance matrix when the sample size is smaller, or not much larger, than the dimensionality of the data, which could potentially be very large. We develop a…
The problem of filtering information from large correlation matrices is of great importance in many applications. We have recently proposed the use of the Kullback-Leibler distance to measure the performance of filtering algorithms in…
Estimation of the precision matrix (or inverse covariance matrix) is of great importance in statistical data analysis and machine learning. However, as the number of parameters scales quadratically with the dimension $p$, computation…
We investigate the complexity of covariance matrix estimation for Gibbs distributions based on dependent samples from a Markov chain. We show that when $\pi$ satisfies a Poincar\'e inequality and the chain possesses a spectral gap, we can…
This manuscript presents an approach to perform generalized linear regression with multiple high dimensional covariance matrices as the outcome. Model parameters are proposed to be estimated by maximizing a pseudo-likelihood. When the data…
In this article, we derive concentration inequalities for the spectral norm of two classical sample estimators of large dimensional Toeplitz covariance matrices, demonstrating in particular their asymptotic almost sure consistence. The…
We establish large sample approximations for an arbitray number of bilinear forms of the sample variance-covariance matrix of a high-dimensional vector time series using $ \ell_1$-bounded and small $\ell_2$-bounded weighting vectors.…