Talagrand, we also show that the exponential integrability of a γ-sub-Gaussian vector in an arbitrary separable Banach space. These two definitions of sub-Gaussian vectors and γ-sub-Gaussian vectors are not comparable, and neither of these definitions is a necessary condition for the exponential...
We study the problem of estimating the mean of a random vector $X$ given a sample of $N$ independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that the second moment of $X$ exists. The estimator is...
This paper considers two sub-optimal transmission schemes for a family of parallel Gaussian vector broadcast channels. One of the schemes is based on the QR precoding of Ginis et al. (2000). In QR precoding, the maximum achievable throughput depends on the order in which users are encoded. ...
We also investigate a random method to identify exactly any vector which has a relatively short support using linear subgaussian measurements as above. It turns out that our analysis, when applied to $\\{-1,1\\}$-valued vectors with i.i.d, symmetric entries, yields new information on the...
The second type of sparsity in a quadratic form comes from the setting where we randomly sample the elements of an anisotropic subgaussian vector Y = H X Y = H X where H \\in \\mathbb{R}^{mimes m} H \\in \\mathbb{R}^{mimes m} is an m imes m m imes m symmetric matrix; ...
The approach applied to a pair of stock index returns demonstrates that such a bivariate vector can be a sample coming from a bivariate sub-Gaussian distribution. The methods presented here can be applied to any nontrivially distributed financial data, among others....
The coefficients of the sparse vector are used as weights to compute weighted features. These features, along with mel frequency cepstral coefficients (MFCC), are used as feature vectors for classification. Experimental results show that the proposed method gives an accuracy as high as 95.6 %, ...
Traditionally, the maximum likelihood estimation of parameters has been considered using a representation of the multivariate stable vector through a multivariate normal vector and an α -stable subordinator. This paper introduces an analytical expectation maximization (EM) algorithm for the estimation of...
We study the problem of estimating the mean of a random vector X given a sample of N independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that the second moment of X exists. The estimator is based on...
Some exponential bounds for the tail probabilities of the norm of a scalar φ-sub-Gaussian random vector are obtained. Using these inequalities, some results on the asymptotic behavior of a sequence (X (n) ) of R d -valued scalar φ-sub-Gaussian random vectors are proved. The interest of...