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The Cross-Entropy Method for Estimation
cross-entropy estimation rare events importance sampling adaptive Monte Carlo zero-variance distribution
2015/7/6
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...
Testing Exponentiality Based on Rényi Entropy With Progressively Type-II Censored Data
Renyi Entropy hazard function Monte Carlo simulation order statistics Type-II progressively censored data
2013/4/28
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...
Refinement revisited with connections to Bayes error, conditional entropy and calibrated classifiers
Refinement Score Probability Elicitation Calibrated Classifier Bayes Error Bound Conditional Entropy Proper Loss
2013/4/27
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...
Statistical estimation of quadratic Rényi entropy for a stationary m-dependent sequence
Entropy estimation quadratic R′enyi entropy stationarym-dependent sequence inter-point distances U-statistics
2013/4/27
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...
Variance estimation and asymptotic confidence bands for the mean estimator of sampled functional data with high entropy unequal probability sampling designs
covariance function finite population Hajek approximation Horvitz-Thompso estimator Kullback-Leibler divergence rejective sampling unequal probability sampling without replacement
2012/11/23
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...
Estimation of entropy-type integral functionals
U-statistics estimation of divergence density power divergence asymptotic normality entropy estimation Raenyi entrop
2012/11/22
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...
Learning Theory Approach to Minimum Error Entropy Criterion
minimum error entropy learning theory Renyi’s entropy empirical risk minimization approximation error
2012/9/18
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...
Scaling of Model Approximation Errors and Expected Entropy Distances
Scaling of Model Approximation Errors Expected Entropy Distances
2012/9/19
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...
Scaling of Model Approximation Errors and Expected Entropy Distances
Scaling of Model Approximation Errors Expected Entropy Distances
2012/9/19
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...
Using Moving Average Method To Estimate Entropy In Testing Exponentiality For Type-II Censored Data
Entropy Monte Carlo simulation Kullback-Leibler distance mov-ing average method Hazard function.
2012/9/19
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 entropy functional, the information path functional's essentials and their connections to Kolmogorov's entropy, complexity and physics
Additive functional Entropy Singularities Natural Border Problem
2011/7/19
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...
Improved estimator of the entropy and goodness of fit tests in ranked set sampling
Ordered Ranked set sampling Judgement ranking Order statistic Information theory
2011/7/5
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...
Estimation of Rényi Entropy and Mutual Information Based on Generalized Nearest-Neighbor Graphs
Rényi Entropy Mutual Information Generalized Nearest-Neighbor Graphs
2010/3/11
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...