| 1. |
- Källberg, David, et al.
(author)
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Statistical estimation of quadratic Rényi entropy for a stationary m-dependent sequence
- 2014
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In: Journal of nonparametric statistics (Print). - : Taylor & Francis. - 1048-5252 .- 1029-0311. ; 26:2, s. 385-411
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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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| 2. |
- Källberg, David, 1982-, et al.
(author)
-
Statistical inference for Rényi entropy functionals
- 2012
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In: Conceptual modelling and its theoretical foundations. - Berlin, Heidelberg : Springer Berlin/Heidelberg. - 9783642282782 - 9783642282799 ; , s. 36-51
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Book chapter (peer-reviewed)abstract
- Numerous entropy-type characteristics (functionals) generalizing Rényi entropy are widely used in mathematical statistics, physics, information theory, and signal processing for characterizing uncertainty in probability distributions and distribution identification problems. We consider estimators of some entropy (integral) functionals for discrete and continuous distributions based on the number of epsilon-close vector records in the corresponding independent and identically distributed samples from two distributions. The proposed estimators are generalized U-statistics. We show the asymptotic properties of these estimators (e.g., consistency and asymptotic normality). The results can be applied in various problems in computer science and mathematical statistics (e.g., approximate matching for random databases, record linkage, image matching).
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| 3. |
- Källberg, David, 1982-, et al.
(author)
-
Statistical modeling for image matching in large image databases
- 2011
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In: 2011 International Conference on Internet of Things and 4th International Conference on Cyber, Physical and Social Computing. - : IEEE. - 9780769545806 ; , s. 648-652
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Conference paper (peer-reviewed)abstract
- Matching a query (reference) image to an image extracted from a database containing (possibly) transformed image copies is an important retrieval task. In this paper we present a general method based on matching densities of the corresponding image feature vectors by using the Bregman distances. We consider statistical estimators for some quEDratic entropy-type characteristics. In particular, the quEDratic Bregman distances can be evaluated in image matching problems whenever images are modeled by random feature vectors in large image databases. Moreover, this method can be used for average case analysis for optimization of joining large databases. © 2011 IEEE.
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| 4. |
- Leonenko, Nikolaj, et al.
(author)
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Statistical inference for the epsilon-entropy and the quadratic Renyi entropy
- 2010
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In: Journal of Multivariate Analysis. - : Elsevier BV. - 0047-259X .- 1095-7243. ; 101:9, s. 1981-1994
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Journal article (peer-reviewed)abstract
- Entropy and its various generalizations are widely used in mathematical statistics, communication theory, physical and computer sciences for characterizing the amount of information in a probability distribution. We consider estimators of the quadratic Rényi entropy and some related characteristics of discrete and continuous probability distributions based on the number of coincident (or-close) vector observations in the corresponding independent and identically distributed sample. We show some asymptotic properties of these estimators (e.g., consistency and asymptotic normality). These estimators can be used in various problems in mathematical statistics and computer science (e.g., distribution identi¯cation problems, average case analysis for random databases, approximate pattern matching in bioinformatics, cryptography).
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