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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Numerical Analysis
- Statistics, Probability and Uncertainty