TY - JOUR
T1 - A central limit theorem for measurements on the logarithmic scale and its application to dimension estimates
AU - Denker, Manfred
AU - Min, Aleksey
N1 - Funding Information:
The research of Aleksey Min was supported by the Graduiertenkolleg “Strömungsinstabilitäten und Turbulenz” at the University of Göttingen. The authors would like to thank two referees for their valuable comments.
PY - 2008/4
Y1 - 2008/4
N2 - 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.
AB - 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.
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U2 - 10.1016/j.jmva.2007.03.005
DO - 10.1016/j.jmva.2007.03.005
M3 - Article
AN - SCOPUS:40749137846
SN - 0047-259X
VL - 99
SP - 665
EP - 683
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
IS - 4
ER -