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On invariant distribution function estimation for continuous-time stationary processes. (English) Zbl 1084.62084
Summary: 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.

62M09 Non-Markovian processes: estimation
62G30 Order statistics; empirical distribution functions
60F17 Functional limit theorems; invariance principles
60G10 Stationary stochastic processes
62G20 Asymptotic properties of nonparametric inference
Full Text: DOI
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