The paper proposes a new covariance estimator for large covariance matrices when the variables have a natural ordering. Using the Cholesky decomposition of the inverse, we impose a banded structure on the Cholesky factor, and select the bandwidth adaptively for each row of the Cholesky factor, using a novel penalty we call nested Lasso. This structure has more flexibility than regular banding, ...

We propose a jump robust positive semidefinite rank-based estimator for the daily covariance matrix using intraday returns. It disentangles covariance estimation into variance and correlation components, allowing to estimate correlations over lower sampling frequencies to account for non-synchronous trading. The efficiency gain of disentangling covariance estimation and the jump robustness of t...

Some connections between linear minimum mean square error estimators, maximum output SNR filters and the least square solutions are presented. The notes have been prepared to be distributed with EE 503 (METU, Electrical Engin.) lecture notes. 1 Linear Minimum Mean Square Error Estimators The following signal model is assumed: r = Hs + v (1) Here r is a N × 1 column vector denoting the observati...

We show that the quantile regression estimator is consistent and asymptotically normal when the error terms are correlated within clusters but independent across clusters. A consistent estimator of the covariance matrix of the asymptotic distribution is provided and we propose a specification test capable of detecting the presence of intra-cluster correlation. A small simulation study illustrat...

The aim of detecting outliers in a multivariate sample can be pursued in diierent ways. We investigate here the performance of several simultaneous multivariate outlier identiication rules based on robust estimators of location and scale. It has been shown that the use of estimators with high nite-sample breakdown point in such procedures yields a good behaviour with respect to the prevention o...

Given i.i.d. observations of a random vector X ∈ R, we study the problem of estimating both its covariance matrix Σ, and its inverse covariance or concentration matrix Θ = (Σ). When X is multivariate Gaussian, the non-zero structure of Θ is specified by the graph of an associated Gaussian Markov random field; and a popular estimator for such sparse Θ is the l1-regularized Gaussian MLE. This est...

Statistical conditional optimization criteria lead to the development of an iterative algorithm that starts from the matched filter (or constraint vector) and generates a sequence of filters that converges to the minimum-variance-distortionless-response (MVDR) solution for any positive definite input autocorrelation matrix. Computationally, the algorithm is a simple, noninvasive, recursive proc...

Nonlinear evolution causes the galaxy power spectrum to become broadly correlated over different wavenumbers. It is shown that prewhitening the power spectrum – transforming the power spectrum in such a way that the noise covariance becomes proportional to the unit matrix – greatly narrows the covariance of power. The eigenfunctions of the covariance of the prewhitened nonlinear power spectrum ...