1,528 research outputs found
On the Efficient Simulation of the Left-Tail of the Sum of Correlated Log-normal Variates
The sum of Log-normal variates is encountered in many challenging
applications such as in performance analysis of wireless communication systems
and in financial engineering. Several approximation methods have been developed
in the literature, the accuracy of which is not ensured in the tail regions.
These regions are of primordial interest wherein small probability values have
to be evaluated with high precision. Variance reduction techniques are known to
yield accurate, yet efficient, estimates of small probability values. Most of
the existing approaches, however, have considered the problem of estimating the
right-tail of the sum of Log-normal random variables (RVS). In the present
work, we consider instead the estimation of the left-tail of the sum of
correlated Log-normal variates with Gaussian copula under a mild assumption on
the covariance matrix. We propose an estimator combining an existing
mean-shifting importance sampling approach with a control variate technique.
The main result is that the proposed estimator has an asymptotically vanishing
relative error which represents a major finding in the context of the left-tail
simulation of the sum of Log-normal RVs. Finally, we assess by various
simulation results the performances of the proposed estimator compared to
existing estimators
On the Sum of Order Statistics and Applications to Wireless Communication Systems Performances
We consider the problem of evaluating the cumulative distribution function
(CDF) of the sum of order statistics, which serves to compute outage
probability (OP) values at the output of generalized selection combining
receivers. Generally, closed-form expressions of the CDF of the sum of order
statistics are unavailable for many practical distributions. Moreover, the
naive Monte Carlo (MC) method requires a substantial computational effort when
the probability of interest is sufficiently small. In the region of small OP
values, we propose instead two effective variance reduction techniques that
yield a reliable estimate of the CDF with small computing cost. The first
estimator, which can be viewed as an importance sampling estimator, has bounded
relative error under a certain assumption that is shown to hold for most of the
challenging distributions. An improvement of this estimator is then proposed
for the Pareto and the Weibull cases. The second is a conditional MC estimator
that achieves the bounded relative error property for the Generalized Gamma
case and the logarithmic efficiency in the Log-normal case. Finally, the
efficiency of these estimators is compared via various numerical experiments
Skellam shrinkage: Wavelet-based intensity estimation for inhomogeneous Poisson data
The ubiquity of integrating detectors in imaging and other applications
implies that a variety of real-world data are well modeled as Poisson random
variables whose means are in turn proportional to an underlying vector-valued
signal of interest. In this article, we first show how the so-called Skellam
distribution arises from the fact that Haar wavelet and filterbank transform
coefficients corresponding to measurements of this type are distributed as sums
and differences of Poisson counts. We then provide two main theorems on Skellam
shrinkage, one showing the near-optimality of shrinkage in the Bayesian setting
and the other providing for unbiased risk estimation in a frequentist context.
These results serve to yield new estimators in the Haar transform domain,
including an unbiased risk estimate for shrinkage of Haar-Fisz
variance-stabilized data, along with accompanying low-complexity algorithms for
inference. We conclude with a simulation study demonstrating the efficacy of
our Skellam shrinkage estimators both for the standard univariate wavelet test
functions as well as a variety of test images taken from the image processing
literature, confirming that they offer substantial performance improvements
over existing alternatives.Comment: 27 pages, 8 figures, slight formatting changes; submitted for
publicatio
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