44 research outputs found
An econophysics approach to analyse uncertainty in financial markets: an application to the Portuguese stock market
In recent years there has been a closer interrelationship between several
scientific areas trying to obtain a more realistic and rich explanation of the
natural and social phenomena. Among these it should be emphasized the
increasing interrelationship between physics and financial theory. In this
field the analysis of uncertainty, which is crucial in financial analysis, can
be made using measures of physics statistics and information theory, namely the
Shannon entropy. One advantage of this approach is that the entropy is a more
general measure than the variance, since it accounts for higher order moments
of a probability distribution function. An empirical application was made using
data collected from the Portuguese Stock Market.Comment: 8 pages, 2 figures, presented in the conference Next Sigma-Phi 200
Finite-Sample Analysis of Fixed-k Nearest Neighbor Density Functional Estimators
We provide finite-sample analysis of a general framework for using k-nearest
neighbor statistics to estimate functionals of a nonparametric continuous
probability density, including entropies and divergences. Rather than plugging
a consistent density estimate (which requires as the sample size
) into the functional of interest, the estimators we consider fix
k and perform a bias correction. This is more efficient computationally, and,
as we show in certain cases, statistically, leading to faster convergence
rates. Our framework unifies several previous estimators, for most of which
ours are the first finite sample guarantees.Comment: 16 pages, 0 figure
Sequence alignment, mutual information, and dissimilarity measures for constructing phylogenies
Existing sequence alignment algorithms use heuristic scoring schemes which
cannot be used as objective distance metrics. Therefore one relies on measures
like the p- or log-det distances, or makes explicit, and often simplistic,
assumptions about sequence evolution. Information theory provides an
alternative, in the form of mutual information (MI) which is, in principle, an
objective and model independent similarity measure. MI can be estimated by
concatenating and zipping sequences, yielding thereby the "normalized
compression distance". So far this has produced promising results, but with
uncontrolled errors. We describe a simple approach to get robust estimates of
MI from global pairwise alignments. Using standard alignment algorithms, this
gives for animal mitochondrial DNA estimates that are strikingly close to
estimates obtained from the alignment free methods mentioned above. Our main
result uses algorithmic (Kolmogorov) information theory, but we show that
similar results can also be obtained from Shannon theory. Due to the fact that
it is not additive, normalized compression distance is not an optimal metric
for phylogenetics, but we propose a simple modification that overcomes the
issue of additivity. We test several versions of our MI based distance measures
on a large number of randomly chosen quartets and demonstrate that they all
perform better than traditional measures like the Kimura or log-det (resp.
paralinear) distances. Even a simplified version based on single letter Shannon
entropies, which can be easily incorporated in existing software packages, gave
superior results throughout the entire animal kingdom. But we see the main
virtue of our approach in a more general way. For example, it can also help to
judge the relative merits of different alignment algorithms, by estimating the
significance of specific alignments.Comment: 19 pages + 16 pages of supplementary materia