(1) Statslab, Wilberforce Road, Cambridge, CB3 0WB, UK;(2) Department of Statistics, Yale University, 208290, New Haven, Connecticut 06520-8290, USA
Abstract:
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 converges to zero.OTJ is a Fellow of Christs College, Cambridge, who helped support two trips to Yale University during which this paper was written.Mathematics Subject Classification (2000):Primary: 62B10 Secondary: 60F05, 94A17