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Contact:
Marcus Greferath
School of Math. Sciences
University College Dublin
Belfield, Dublin 4, Ireland
Phone:
+353-1-716-2588 (UCD)
+353-85-153-0951 (mobile)
Joachim Rosenthal
Institut of Mathematics
University of Zurich
Winterthurerstrasse 190
8057 Zurich, Switzerland
Phone:
+41-44-63 55884 (office)
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ITW 2010 Dublin
IEEE Information Theory Workshop
Dublin, August 30 - September 3, 2010
Estimation and portfolio theory
Thu 2 Sep, 09.55-11.15, Room 2
Contributed session
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Siu-Wai Ho, Terence Chan, and Alex Grant
The Confidence Interval of Entropy Estimation through a Noisy Channel
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Abstract:
Suppose a stationary memoryless source is observed through a
discrete memoryless channel. Determining analytical confidence
intervals on the source entropy is known to be a difficult problem,
even when the observation channel is noiseless. In this paper, we
determine confidence intervals for estimation of source entropy over
discrete memoryless channels with invertible transition matrices. A
lower bound is given for the minimum number of samples required to
guarantee a desired confidence interval. All these results do not
require any prior knowledge of the source distribution, other than
the alphabet size. When the alphabet size is countably infinite or
unknown, we illustrate an inherent difficulty in estimating the
source entropy.
Thu 2 Sep, 09.55-10.15, Room 2
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Emrah Akyol, Kumar Viswanatha, and Kenneth Rose
On Conditions for Linearity of Optimal Estimation
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Abstract:
When is optimal estimation linear? It is well-known that, in the
case of a Gaussian source contaminated with Gaussian noise, a linear
estimator minimizes the mean square estimation error. This paper
analyzes more generally the conditions for linearity of optimal
estimators. Given a noise (or source) distribution, and a specified
signal to noise ratio (SNR), we derive conditions for existence and
uniqueness of a source (or noise) distribution that renders the
Lp norm optimal estimator linear. We then show that, if the noise
and source variances are equal, then the matching source is
distributed identically to the noise. Moreover, we prove that the
Gaussian source-channel pair is unique in that it is the only
source-channel pair for which the MSE optimal estimator is linear at
more than one SNR values.
Thu 2 Sep, 10.15-10.35, Room 2
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Jayakrishnan Unnikrishnan, Sean Meyn, and Venugopal V. Veeravalli
On Thresholds for Robust Goodness-of-Fit Tests
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Abstract:
Goodness-of-fit tests are statistical procedures used to test the
hypothesis H0 that a set of observations were drawn according
to some given probability distribution. Decision thresholds used in
goodness-of-fit tests are typically set for guaranteeing a target
false-alarm probability. In many popular testing procedures results
on the weak convergence of the test statistics are used for setting
approximate thresholds when exact computation is infeasible. In this
work, we study robust procedures for goodness-of-fit where accurate
models are not available for the distribution of the observations
under hypothesis H0. We develop procedures for setting
thresholds in two specific examples - a robust version of the
Kolmogorov-Smirnov test for continuous alphabets and a robust
version of the Hoeffding test for finite alphabets.
Thu 2 Sep, 10.35-10.55, Room 2
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Ami Tavory and Meir Feder
Universal Portfolio Algorithms in Realistic-Outcome Markets
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Abstract:
Universal portfolio algorithms find investment strategies
competitive against any CRP (constant rebalanced portfolio)
for each and every market sequence. This work studies the problem of
competitiveness over a subset of realistic, non-pathological, market
sequences observed in many settings, e.g., high-frequency
trading. Competitive investment in this setting will be shown to be
more an extension of the easier universal 0-1 loss problem than of
universal gambling (or coding). Analysis of realism-agnostic
investment algorithms will show that they perform much better on
in-hindsight realistic sequences than previously demonstrated. We
suggest that this implies that the study of realistic universal
portfolio algorithms must involve a comparison to a stronger
adversary than the CRP adversary: an adversary that rebalances a
portfolio often enough to avoid pathological sequences, but not so
frequently that transaction costs dominate.
Thu 2 Sep, 10.55-11.15, Room 2
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