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This chapter describes how difficult statistical estimation problems can often be solved efficiently by means of the cross-entropy (CE) method. The CE method can be viewed as an adaptive importance sa...
In this note the relation between the range-renewal speed and entropy for i.i.d. models is discussed.
For the evaluation of information flow in bivariate time series, information measures have been employed, such as the transfer entropy (TE), the symbolic transfer entropy (STE), defined similarly to T...
We express the joint R\'enyi entropy of progressively censored order statistics in terms of an incomplete integral of the hazard function, and provide a simple estimate of the joint R\'enyi entropy of...
The concept of refinement from probability elicitation is considered for proper scoring rules. Taking directions from the axioms of probability, refinement is further clarified using a Hilbert space i...
The R\'enyi entropy is a generalization of the Shannon entropy and is widely used in mathematical statistics and applied sciences for quantifying the uncertainty in a probability distribution. We cons...
For fixed size sampling designs with high entropy it is well known that the variance of the Horvitz-Thompson estimator can be approximated by the H\'ajek formula. The interest of this asymptotic varia...
Integrated powers of densities of one- or two-multidimensional random variables appear in a variety of problems in mathematical statistics, information theory, and computer science. We study U-statist...
We consider the minimum error entropy (MEE) criterion and anempirical risk minimization learning algorithm in a regression setting. Alearning theory approach is presented for this MEE algorithm and ex...
We compute the expected value of the Kullback-Leibler divergence to various fundamental statistical models with respect to canonical priors on the probability simplex. This yields information about th...
We compute the expected value of the Kullback-Leibler divergence to various fundamental statistical models with respect to canonical priors on the probability simplex. This yields information about th...
In this paper, we introduce a modified test statistic, by applying moving average method and present a new cdf estimator to estimate the joint entropy of the type-II censored data. We also establish a...
The paper introduces the recent results related to an entropy functional on trajectories of a controlled diffusion process, and the information path functional (IPF), analyzing their connections to th...
The entropy is one of the most applicable uncertainty measures in many statistical and en- gineering problems. In statistical literature, the entropy is used in calculation of the Kullback- Leibler (K...
In this paper we consider simple and computationally efficient nonparametric estimators of R´enyi entropy and mutual information based on an i.i.d. sample drawn from an unknown, absolutely con...

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