Displaying similar documents to “Local superefficiency of data-driven projection density estimators in continuous time.”

Change-point estimation from indirect observations. 1. Minimax complexity

A. Goldenshluger, A. Juditsky, A. B. Tsybakov, A. Zeevi (2008)

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

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We consider the problem of nonparametric estimation of signal singularities from indirect and noisy observations. Here by singularity, we mean a discontinuity (change-point) of the signal or of its derivative. The model of indirect observations we consider is that of a linear transform of the signal, observed in white noise. The estimation problem is analyzed in a minimax framework. We provide lower bounds for minimax risks and propose rate-optimal estimation procedures.

Change-point estimation from indirect observations. 2. Adaptation

A. Goldenshluger, A. Juditsky, A. Tsybakov, A. Zeevi (2008)

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

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We focus on the problem of adaptive estimation of signal singularities from indirect and noisy observations. A typical example of such a singularity is a discontinuity (change-point) of the signal or of its derivative. We develop a change-point estimator which adapts to the unknown smoothness of a nuisance deterministic component and to an unknown jump amplitude. We show that the proposed estimator attains optimal adaptive rates of convergence. A simulation study demonstrates reasonable...

On the mean values of Dedekind sums

Wenpeng Zhang (1996)

Journal de théorie des nombres de Bordeaux

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In this paper we study the asymptotic behavior of the mean value of Dedekind sums, and give a sharper asymptotic formula.

Second-order asymptotic expansion for a non-synchronous covariation estimator

Arnak Dalalyan, Nakahiro Yoshida (2011)

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

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In this paper, we consider the problem of estimating the covariation of two diffusion processes when observations are subject to non-synchronicity. Building on recent papers [ (2005) 359–379, (2008) 367–406], we derive second-order asymptotic expansions for the distribution of the Hayashi–Yoshida estimator in a fairly general setup including random sampling schemes and non-anticipative random drifts. The key steps leading to our results are a second-order...