Open Access
October 2005 On invariant distribution function estimation for continuous-time stationary processes
Dominique Dehay
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Bernoulli 11(5): 933-948 (October 2005). DOI: 10.3150/bj/1130077600


This paper is concerned with the asymptotic behaviour of the empirical distribution function for a large class of continuous-time weakly dependent 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. We propose a consistent estimator of the asymptotic variance, and then study the functional central limit theorem for the empirical distribution function.


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Dominique Dehay. "On invariant distribution function estimation for continuous-time stationary processes." Bernoulli 11 (5) 933 - 948, October 2005.


Published: October 2005
First available in Project Euclid: 23 October 2005

zbMATH: 1084.62084
MathSciNet: MR2172847
Digital Object Identifier: 10.3150/bj/1130077600

Keywords: asymptotic normality , central limit theorem , consistency , continuous time , Empirical distribution function , mixing condition , stationary process , weak convergence

Rights: Copyright © 2005 Bernoulli Society for Mathematical Statistics and Probability

Vol.11 • No. 5 • October 2005
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