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When methods of moments are used for identification of power spectral densities, a model is matched to estimated second order statistics such as, e.g., covariance estimates. If the estimates are good there is an infinite family of power…
We propose a distributionally robust formulation for simultaneously estimating the covariance matrix and the precision matrix of a random vector.The proposed model minimizes the worst-case weighted sum of the Frobenius loss of the…
The problem of scheduling sensor transmissions for the detection of correlated random fields using spatially deployed sensors is considered. Using the large deviations principle, a closed-form expression for the error exponent of the miss…
This article deals with the numerical approximation of effective coefficients in stochastic homogenization of discrete linear elliptic equations. The originality of this work is the use of a well-known abstract spectral representation…
The density function of the limiting spectral distribution of general sample covariance matrices is usually unknown. We propose to use kernel estimators which are proved to be consistent. A simulation study is also conducted to show the…
The exact meaning of the noise spectrum of eigenvalues of the covariance matrix is discussed. In order to better understand the possible phenomena behind the observed noise, the spectrum of eigenvalues of the covariance matrix is studied…
We study the accuracy of estimating the covariance and the precision matrix of a $D$-variate sub-Gaussian distribution along a prescribed subspace or direction using the finite sample covariance. Our results show that the estimation…
We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order of magnitude is derived for spectral radius of sample covariance matrices. We also consider a thresholded covariance matrix…
We develop a framework for spectrum sensing in cooperative amplify-and-forward cognitive radio networks. We consider a stochastic model where relays are assigned in cognitive radio networks to transmit the primary user's signal to a…
We investigate the potential of quickest detection based on the eigenvalues of the sample covariance matrix for spectrum sensing applications. A simple phase shift keying (PSK) model with additive white Gaussian noise (AWGN), with $1$…
In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…
In this paper, we consider the spectrum sensing in cognitive radio networks when the impulsive noise appears. We propose a class of blind and robust detectors using M-estimators in eigenvalue based spectrum sensing method. The conventional…
Measuring the power spectral density of a stochastic process, such as a stochastic force or magnetic field, is a fundamental task in many sensing applications. Quantum noise is becoming a major limiting factor to such a task in future…
Given $iid$ observations from an unknown absolute continuous distribution defined on some domain $\Omega$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function.…
Distributionally robust optimization (DRO) has been introduced for solving stochastic programs where the distribution of the random parameters is unknown and must be estimated by samples from that distribution. A key element of DRO is the…
Memory-based collaborative filtering methods like user or item k-nearest neighbors (kNN) are a simple yet effective solution to the recommendation problem. The backbone of these methods is the estimation of the empirical similarity between…
This article provides a central limit theorem for a consistent estimator of population eigenvalues with large multiplicities based on sample covariance matrices. The focus is on limited sample size situations, whereby the number of…
The ensemble covariance matrix of a wide sense stationary signal spatially sampled by a full linear array is positive semi-definite and Toeplitz. However, the direct augmented covariance matrix of an augmentable sparse array is Toeplitz but…
This paper extends some approximation methods that are used to identify closed form Bit Error Rate (BER) expressions which are frequently utilized in investigation and comparison of performance for wireless communication systems in the…
We provide an efficient method to approximate the covariance between decision variables and uncertain parameters in solutions to a general class of stochastic nonlinear complementarity problems. We also develop a sensitivity metric to…