A central limit theorem for measurements on the logarithmic scale and its application to dimension estimates

Manfred Denker, Aleksey Min

Research output: Contribution to journalArticle


We show consistency and asymptotic normality of certain estimators for expected exponential growth rates under i.i.d. observations. These statistical functionals are of the formT (F) = ∫ log ∫ h (x, y) F (d x) F (d y)and are applicable to dimension estimates (information dimension), entropy estimates and estimations of the growth rate of "generating" functions. We also give an affirmative answer to a question posed by Keller in 1997 [A new estimator for information dimension with standard errors and confidence intervals, Stochastic Process. Appl. 71(2):187-206] whether this estimator, specialized for dimension, is an alternative to standard procedures.

Original languageEnglish (US)
Pages (from-to)665-683
Number of pages19
JournalJournal of Multivariate Analysis
Issue number4
Publication statusPublished - Apr 1 2008


All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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