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

Manfred Denker and Aleksey Min

Journal of Multivariate Analysis, 2008, vol. 99, issue 4, 665-683

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)=[integral operator]log[integral operator]h(x,y)F(dx)F(dy)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.

Keywords: Information; dimension; Local; dimension; Central; limit; theorem; U-statistics (search for similar items in EconPapers)
Date: 2008
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