This paper presents a theoretical analysis of the effect of constellation shaping in the transmitter on multimodulus (MMA) blind equalization in the receiver. Constellation shaping reduces average signal energy by a non-uniform distribution of constellation point utilization. Optimal transmit efficiency is achieved by a Gaussian distribution but many blind equalization algorithms require a non-...

A nonlinear random walk related to the porous medium equation (nonlinear Fokker–Planck equation) is investigated. This random walk is such that when the number of steps is sufficiently large, the probability of finding the walker in a certain position after taking a determined number of steps approximates to a q-Gaussian distribution (Gq,β(x) ∝ [1− (1− q)βx2]1/(1−q)), which is a solution of the...

This research estimates portfolio VaR (Value-at-Risk) on G7 exchange rates using a GJR-GARCH-EVT (extreme value theory)-Copula based approach. We first extracts the filtered residuals from each return series via an asymmetric GJR-GARCH model, then constructs the semi-parametric empirical marginal cumulative distribution function (CDF) of each asset using a Gaussian kernel estimate for the inter...

The problem of low-rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to follow a Gaussian distribution with zero mean and a common precision matrix, and a Wishart distribution is specified as a hyperprior over the precision matrix. W...

We derive the exact statistical distribution of maximum a posteriori (MAP) estimators having edge-preserving nonGaussian priors. Such estimators have been widely advocated for image restoration and reconstruction problems. Previous investigations of these image recovery methods have been primarily empirical; the distribution we derive enables theoretical analysis. The signal model is linear wit...

Pencils of Hankel matrices whose elements have a joint Gaussian distribution with nonzero mean and not identical covariance are considered. An approximation to the distribution of the squared modulus of their determinant is computed which allows to get a closed form approximation of the condensed density of the generalized eigenvalues of the pencils. Implications of this result for solving seve...

In this document the generalized hyperbolic (GH) distribution is explained to the extent which is required to understand the internals of the R package ghyp. Essentially, the density and moment generating functions of the GH distribution and its special cases are provided together with some important properties of the GH family. In addition the algorithm underlying the fitting procedure for the...

In this paper, we establish sharp bounds on the joint distribution of potential outcomes and the distribution of treatment effects in parametric switching regimes models with generalized hyperbolic errors and in the semiparametric switching regimes models of Heckman (1990). Our results for parametric switching regimes models with generalized hyperbolic errors extend some existing results for Ga...

We consider the notion of canonical attacks, which are the cryptographic analog of the canonical forms of a one-mode Gaussian channel. Using this notion, we explore the connections between the degradability properties of the channel and its security for quantum key distribution. Finally, we also show some relations between canonical attacks and optimal Gaussian cloners.