69 research outputs found
Two Measures of Dependence
Two families of dependence measures between random variables are introduced.
They are based on the R\'enyi divergence of order and the relative
-entropy, respectively, and both dependence measures reduce to
Shannon's mutual information when their order is one. The first
measure shares many properties with the mutual information, including the
data-processing inequality, and can be related to the optimal error exponents
in composite hypothesis testing. The second measure does not satisfy the
data-processing inequality, but appears naturally in the context of distributed
task encoding.Comment: 40 pages; 1 figure; published in Entrop
Asymptotic behavior of measures of dependence for ARMA(1,2) models with stable innovations. Stationary and non-stationary coefficients
We derive the asymptotic behavior of two measures of dependence (Codifference and Covariation) for ARMA(1,2) models with symmetric alpha-stable innovations and non-stationary coefficients.ARMA model; Stable distribution; Codifference; Covariation;
Estimation and comparison of signed symmetric covariation coefficient and generalized association parameter for alpha-stable dependence modeling
Accepté à Communications in Statistics - Theory and methodsInternational audienceIn this paper we study the estimators of two measures of dependence: the signed symmetric covariation coefficient proposed by Garel and Kodia and the generalized association parameter put forward by Paulauskas. In the sub-Gaussian case, the signed symmetric covariation coefficient and the generalized association parameter coincide. The estimator of the signed symmetric covariation coefficient proposed here is based on fractional lower-order moments. The estimator of the generalized association parameter is based on estimation of a stable spectral measure. We investigate the relative performance of these estimators by comparing results from simulations
Conditional R\'enyi entropy and the relationships between R\'enyi capacities
The analogues of Arimoto's definition of conditional R\'enyi entropy and
R\'enyi mutual information are explored for abstract alphabets. These
quantities, although dependent on the reference measure, have some useful
properties similar to those known in the discrete setting. In addition to
laying out some such basic properties and the relations to R\'enyi divergences,
the relationships between the families of mutual informations defined by
Sibson, Augustin-Csisz\'ar, and Lapidoth-Pfister, as well as the corresponding
capacities, are explored.Comment: 17 pages, 1 figur
Temporal structure and gain/loss asymmetry for real and artificial stock indices
We demonstrate that the gain/loss asymmetry observed for stock indices
vanishes if the temporal dependence structure is destroyed by scrambling the
time series. We also show that an artificial index constructed by a simple
average of a number of individual stocks display gain/loss asymmetry - this
allows us to explicitly analyze the dependence between the index constituents.
We consider mutual information and correlation based measures and show that the
stock returns indeed have a higher degree of dependence in times of market
downturns than upturns
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