ON INVARIANT DISTRIBUTION FUNCTION ESTIMATION
FOR A CLASS OF STATIONARY PROCESSES


Dominique DEHAY
Universite Rennes 2
Rennes, France



ABSTRACT

This work concerns the asymptotic behaviour of the empirical distribution function for a large class of weakly dependent continuous-time stationary processes. Under mild mixing conditions the empirical distribution function is an unbiased consistent estimator of the marginal distribution function of the process. For strongly mixing processes this estimator is asymptotically normal. In this paper we propose a consistent estimator of the asymptotic variance. Then we study the functional central limit theorem for the empirical distribution function.



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