Displaying similar documents to “Second-order asymptotic expansion for a non-synchronous covariation estimator”

LAMN property for hidden processes : the case of integrated diffusions

Arnaud Gloter, Emmanuel Gobet (2008)

Annales de l'I.H.P. Probabilités et statistiques

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In this paper we prove the Local Asymptotic Mixed Normality (LAMN) property for the statistical model given by the observation of local means of a diffusion process . Our data are given by  d() for =0, …, −1 and the unknown parameter appears in the diffusion coefficient of the process only. Although the data are neither markovian nor gaussian we can write down, with help of Malliavin calculus, an explicit expression for...

Irregular sampling and central limit theorems for power variations : the continuous case

Takaki Hayashi, Jean Jacod, Nakahiro Yoshida (2011)

Annales de l'I.H.P. Probabilités et statistiques

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In the context of high frequency data, one often has to deal with observations occurring at irregularly spaced times, at transaction times for example in finance. Here we examine how the estimation of the squared or other powers of the volatility is affected by irregularly spaced data. The emphasis is on the kind of assumptions on the sampling scheme which allow to provide consistent estimators, together with an associated central limit theorem, and especially when the sampling scheme...

On the density of some Wiener functionals: an application of Malliavin calculus.

Antoni Sintes Blanc (1992)

Publicacions Matemàtiques

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Using a representation as an infinite linear combination of chi-square independent random variables, it is shown that some Wiener functionals, appearing in empirical characteristic process asymptotic theory, have densities which are tempered in the properly infinite case and exponentially decaying in the finite case.

Local superefficiency of data-driven projection density estimators in continuous time.

Denis Bosq, Delphine Blanke (2004)

SORT

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We construct a data-driven projection density estimator for continuous time processes. This estimator reaches superoptimal rates over a class F of densities that is dense in the family of all possible densities, and a «reasonable» rate elsewhere. The class F may be chosen previously by the analyst. Results apply to R-valued processes and to N-valued processes. In the particular case where square-integrable local time does exist, it is shown that our estimator is strictly better than...