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1.	Källberg, David, et al. (author) Statistical estimation of quadratic Rényi entropy for a stationary m-dependent sequence 2014 In: Journal of nonparametric statistics (Print). - : Taylor & Francis. - 1048-5252 .- 1029-0311. ; 26:2, s. 385-411 Journal article (peer-reviewed)abstract The Rényi 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 consider estimation of the quadratic Rényi entropy and related functionals for the marginal distribution of a stationary m-dependent sequence. The U-statistic estimators under study are based on the number of ε-close vector observations in the corresponding sample. A variety of asymptotic properties for these estimators are obtained (e.g., consistency, asymptotic normality, Poisson convergence). The results can be used in diverse statistical and computer science problems whenever the conventional independence assumption is too strong (e.g., ε-keys in time series databases, distribution identication problems for dependent samples).

Källberg, David, et al. (author)
Statistical estimation of quadratic Rényi entropy for a stationary m-dependent sequence
2014
In: Journal of nonparametric statistics (Print). - : Taylor & Francis. - 1048-5252 .- 1029-0311. ; 26:2, s. 385-411
Journal article (peer-reviewed)abstract
- The Rényi 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 consider estimation of the quadratic Rényi entropy and related functionals for the marginal distribution of a stationary m-dependent sequence. The U-statistic estimators under study are based on the number of ε-close vector observations in the corresponding sample. A variety of asymptotic properties for these estimators are obtained (e.g., consistency, asymptotic normality, Poisson convergence). The results can be used in diverse statistical and computer science problems whenever the conventional independence assumption is too strong (e.g., ε-keys in time series databases, distribution identication problems for dependent samples).

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