Abstract
Nonuniform rates of convergence to normality are studied for standardised sample sum for some stationary m dependent processes when i) some finite moment of order⩾ 2 exists, ii) when all the finite order moments exist but moment generating function of the individual random variables may not exist. These rates are then used to compute the probabilities of deviations and certain moment type convergences. Possible extensions of the results to non-stationary m-dependent processes are indicated.
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