Displaying similar documents to “Shrinkage strategies in some multiple multi-factor dynamical systems”

Shrinkage strategies in some multiple multi-factor dynamical systems

Sévérien Nkurunziza (2012)

ESAIM: Probability and Statistics

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In this paper, we are interested in estimation problem for the drift parameters matrices of independent multivariate diffusion processes. More specifically, we consider the case where the -parameters matrices are supposed to satisfy some uncertain constraints. Given such an uncertainty, we develop shrinkage estimators which improve over the performance of the maximum likelihood estimator (MLE). Under an asymptotic distributional quadratic risk criterion, we study the relative dominance...

Nonparametric estimation of the density of the alternative hypothesis in a multiple testing setup. Application to local false discovery rate estimation

Van Hanh Nguyen, Catherine Matias (2014)

ESAIM: Probability and Statistics

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In a multiple testing context, we consider a semiparametric mixture model with two components where one component is known and corresponds to the distribution of -values under the null hypothesis and the other component is nonparametric and stands for the distribution under the alternative hypothesis. Motivated by the issue of local false discovery rate estimation, we focus here on the estimation of the nonparametric unknown component in the mixture, relying on a preliminary estimator...

Adaptive estimation of a density function using beta kernels

Karine Bertin, Nicolas Klutchnikoff (2014)

ESAIM: Probability and Statistics

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In this paper we are interested in the estimation of a density − defined on a compact interval of ℝ− from independent and identically distributed observations. In order to avoid boundary effect, beta kernel estimators are used and we propose a procedure (inspired by Lepski’s method) in order to select the bandwidth. Our procedure is proved to be adaptive in an asymptotically minimax framework. Our estimator is compared with both the cross-validation algorithm and the oracle estimator...

Zienkiewicz–Zhu error estimators on anisotropic tetrahedral and triangular finite element meshes

Gerd Kunert, Serge Nicaise (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider error estimators that can be applied to tetrahedral finite element meshes,  meshes where the aspect ratio of the elements can be arbitrarily large. Two kinds of Zienkiewicz–Zhu (ZZ) type error estimators are derived which originate from different backgrounds. In the course of the analysis, the first estimator turns out to be a special case of the second one, and both estimators can be expressed using some recovered gradient. The advantage of keeping two different analyses...

Penalized nonparametric drift estimation for a continuously observed one-dimensional diffusion process

Eva Löcherbach, Dasha Loukianova, Oleg Loukianov (2011)

ESAIM: Probability and Statistics

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Let be a one dimensional positive recurrent diffusion continuously observed on [0,] . We consider a non parametric estimator of the drift function on a given interval. Our estimator, obtained using a penalized least square approach, belongs to a finite dimensional functional space, whose dimension is selected according to the data. The non-asymptotic risk-bound reaches the minimax optimal rate of convergence when → ∞. The main point of our work is that we do not suppose the process...

Penalized nonparametric drift estimation for a continuously observed one-dimensional diffusion process

Eva Löcherbach, Dasha Loukianova, Oleg Loukianov (2012)

ESAIM: Probability and Statistics

Similarity:

Let be a one dimensional positive recurrent diffusion continuously observed on [0,] . We consider a non parametric estimator of the drift function on a given interval. Our estimator, obtained using a penalized least square approach, belongs to a finite dimensional functional space, whose dimension is selected according to the data. The non-asymptotic risk-bound reaches the minimax optimal rate of convergence when → ∞. The main point of our work is that we do not suppose the process...