Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series A, Pt. 2, 259--266

SHARPER SPEED OF CONVERGENCE TO NORMALITY FOR SOME $M$ DEPENDENT PROCESSES

By

RATAN DASGUPTA, *Indian Statistical Institute*

SUMMARY. For a stationary *m* dependent process under certain assumptions which ensure that the individual random variables have finite moment generating function but the random variables may not be bounded, the non-uniform rates of convergence of standardised sample sum to normality are studied. The results obtained turn out to be quite sharp even for i.i.d random variables. Application of these rates are made in moment type convergences, l_{q} versions of the Berry-Esseen theorem and to probabilities of deviations. Possible extensions are indicated for non-stationary *m* dependent processes. The conditions assumed are shown to be fulfilled for moving average process.

*AMS (1980) subject classification.* 60F05,60F10,60G10

*Key words and phrases*. $L_p$ version of Berry-Esseen theorem, moving average process