Estimation of entropy-type integral functionals
2016 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 45, no 4, 887-905 p.Article in journal (Other academic) Published
Entropy-type integral functionals of densities are widely used in mathematical statistics, information theory, and computer science. Examples include measures of closeness between distributions (e.g., density power divergence) and uncertainty characteristics for a random variable (e.g., Renyi entropy). In this paper, we study U-statistic estimators for a class of such functionals. The estimators are based on ε-close vector observations in the corresponding independent and identically distributed samples. We prove asymptotic properties of the estimators (consistency and asymptotic normality) under mild integrability and smoothness conditions for the densities. The results can be applied in diverse problems in mathematical statistics and computer science (e.g., distribution identication problems, approximate matching for random databases, two-sample problems).
Place, publisher, year, edition, pages
2016. Vol. 45, no 4, 887-905 p.
Divergence estimation, asymptotic normality, U-statistics, inter-point distances, quadratic functional, entropy estimation
Probability Theory and Statistics
Research subject Mathematical Statistics
IdentifiersURN: urn:nbn:se:umu:diva-60993DOI: 10.1080/03610926.2013.853789ISI: 000370612900005OAI: oai:DiVA.org:umu-60993DiVA: diva2:565242