8 Information inequalities and a dependent Central Limit Theorem Oliver Johnson

J ul 2 00 3 Fisher Information inequalities and the Central Limit Theorem Oliver

We give conditions for an O(1/n) rate of convergence of Fisher information and relative entropy in the Central Limit Theorem. We use the theory of projections in L2 spaces and Poincaré inequalities, to provide a better understanding of the decrease in Fisher Information implied by results of Barron and Brown. We show that if the standardized Fisher Information ever becomes finite then it conver...

N ov 2 00 1 Fisher Information inequalities and the Central Limit Theorem Oliver

We give conditions for an O(1/n) rate of convergence of Fisher information and relative entropy in the Central Limit Theorem. We use the theory of projections in L2 spaces and Poincaré inequalities, to provide a better understanding of the decrease in Fisher information implied by results of Barron and Brown. We show that if the standardized Fisher information ever becomes finite then it conver...

Central and Local Limit Theories in Markov Dependent Random Variables

Density Estimators for Truncated Dependent Data

In some long term studies, a series of dependent and possibly truncated lifetime data may be observed. Suppose that the lifetimes have a common continuous distribution function F. A popular stochastic measure of the distance between the density function f of the lifetimes and its kernel estimate fn is the integrated square error (ISE). In this paper, we derive a central limit theorem for t...

Entropy inequalities and the Central Limit Theorem

Motivated by Barron (1986, Ann. Probab. 14, 336–342), Brown (1982, Statistics and Probability: Essays in Honour of C.R. Rao, pp. 141–148) and Carlen and So er (1991, Comm. Math. Phys. 140, 339–371), we prove a version of the Lindeberg–Feller Theorem, showing normal convergence of the normalised sum of independent, not necessarily identically distributed random variables, under standard conditio...