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 form T(F)=int(log(int(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.     «

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 form T(F)=int(log(int(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...     »