Estimation of entropy-type integral functionals

• 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).

Ämnesord

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Nyckelord

Divergence estimation

asymptotic normality

U-statistics

inter-point distances

quadratic functional

entropy estimation

matematisk statistik

Mathematical Statistics

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