Renyi entropy9/7/2023 ![]() ![]() The consistency of the estimators is obtained under weaker density assumptions. In Paper B, we provide some important generalizations of the results for continuous distributions in Paper A. Applications of the obtained results related to entropy maximizing distributions, stochastic databases, and image matching are discussed. We prove some asymptotic properties of the estimators such as consistency and asymptotic normality. We propose U-statistic estimators of these functionals based on the coincident or epsilon-close vector observations in the corresponding independent and identically distributed samples. In Paper A, we consider a general class of entropy-type functionals which includes, for example, integer order Rényi entropy and certain Bregman divergences. The thesis consists of an introductory survey of the subject and some related theory and four papers (A-D). We consider estimation from both independent and dependent observations. Asymptotic properties of particular nonparametric estimators of such functionals are investigated. In this thesis, we study statistical inference for entropy, divergence, and related functionals of one or two probability distributions. Probability Theory and Statistics Research subject Mathematical Statistics Identifiers URN: urn:nbn:se:umu:diva-79958 DOI: 10.1080/10485252.2013.854438 ISI: 000334160600011 Scopus ID: 2-s2.0-84893178465 OAI: oai::umu-79958 DiVA, id: diva2:645449Ģ013 (English) Doctoral thesis, comprehensive summary (Other academic) Alternative title Icke-parametrisk statistisk inferens för entropirelaterade funktionaler 385-411Įntropy estimation, quadratic Rényi entropy, stationary m-dependent sequence, U-statistics, inter-point distances National Category ![]() Place, publisher, year, edition, pagesTaylor & Francis, 2014. 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). A variety of asymptotic properties for these estimators are obtained (e.g., consistency, asymptotic normality, Poisson convergence). The U-statistic estimators under study are based on the number of ε-close vector observations in the corresponding sample. We consider estimation of the quadratic Rényi entropy and related functionals for the marginal distribution of a stationary m-dependent sequence. 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. 385-411 Article in journal (Refereed) Published Abstract ![]()
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