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

Manfred Heinz Denker, Aleksey Min

Research output: Contribution to journalArticle

Abstract

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
Volume99
Issue number4
DOIs
StatePublished - Apr 1 2008

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Central limit theorem
Logarithmic
Random processes
Estimator
Estimate
Entropy
Exponential Growth
Standard error
Asymptotic Normality
Generating Function
Confidence interval
Stochastic Processes
Alternatives

All Science Journal Classification (ASJC) codes

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

Cite this

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A central limit theorem for measurements on the logarithmic scale and its application to dimension estimates. / Denker, Manfred Heinz; Min, Aleksey.

In: Journal of Multivariate Analysis, Vol. 99, No. 4, 01.04.2008, p. 665-683.

Research output: Contribution to journalArticle

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