Approximation of density functions by sequences of exponential families

DOI10.1214/aos/1176348252zbMath0739.62027OpenAlexW2040335964MaRDI QIDQ1178945

Publication date: 26 June 1992

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1176348252

zbMATH Keywords

splines polynomials maximum likelihood convergence results density estimation principle of maximum entropy trigonometric series Kullback-Leibler distance regular exponential family minimum relative entropy basis functions expansion \(L2\)-approximation log-density functions square-integrable derivatives

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Statistical aspects of information-theoretic topics (62B10)

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