Bernoulli

  • Bernoulli
  • Volume 11, Number 5 (2005), 933-948.

On invariant distribution function estimation for continuous-time stationary processes

Dominique Dehay

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Abstract

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.

Article information

Source
Bernoulli, Volume 11, Number 5 (2005), 933-948.

Dates
First available in Project Euclid: 23 October 2005

Permanent link to this document
https://projecteuclid.org/euclid.bj/1130077600

Digital Object Identifier
doi:10.3150/bj/1130077600

Mathematical Reviews number (MathSciNet)
MR2172847

Zentralblatt MATH identifier
1084.62084

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

Citation

Dehay, Dominique. On invariant distribution function estimation for continuous-time stationary processes. Bernoulli 11 (2005), no. 5, 933--948. doi:10.3150/bj/1130077600. https://projecteuclid.org/euclid.bj/1130077600


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