Extreme values and kernel estimates of point processes boundaries

Stéphane Girard; Pierre Jacob

Displaying similar documents to “Extreme values and kernel estimates of point processes boundaries”

Exact adaptive pointwise estimation on Sobolev classes of densities

Cristina Butucea (2001)

ESAIM: Probability and Statistics

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The subject of this paper is to estimate adaptively the common probability density of $n$ independent, identically distributed random variables. The estimation is done at a fixed point $x_{0} \in ℝ$ , over the density functions that belong to the Sobolev class $W_{n} (β, L)$ . We consider the adaptive problem setup, where the regularity parameter $β$ is unknown and varies in a given set $B_{n}$ . A sharp adaptive estimator is obtained, and the explicit asymptotical constant, associated to its rate of convergence is found. ...

Central limit theorem of the smoothed empirical distribution functions for asymptotically stationary absolutely regular stochastic processes.

Elharfaoui, Echarif, Harel, Michel (2008)

Journal of Applied Mathematics and Stochastic Analysis

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Mean square error for histograms when estimating Radon-Nikodym derivatives.

Oliveira, P.E. (2000)

Portugaliae Mathematica

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Diffusions with measurement errors. II. Optimal estimators

Arnaud Gloter, Jean Jacod (2001)

ESAIM: Probability and Statistics

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We consider a diffusion process $X$ which is observed at times $i / n$ for $i = 0, 1, ..., n$ , each observation being subject to a measurement error. All errors are independent and centered gaussian with known variance $ρ_{n}$ . There is an unknown parameter to estimate within the diffusion coefficient. In this second paper we construct estimators which are asymptotically optimal when the process $X$ is a gaussian martingale, and we conjecture that they are also optimal in the general case.

Free area estimation in a dynamic germ-grain model with renewal dropping process.

de Giosa, Marcello (2006)

Journal of Applied Mathematics and Stochastic Analysis

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Multidimensional limit theorems for smoothed extreme value estimates of point processes boundaries

Ludovic Menneteau (2008)

ESAIM: Probability and Statistics

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In this paper, we give sufficient conditions to establish central limit theorems and moderate deviation principle for a class of support estimates of empirical and Poisson point processes. The considered estimates are obtained by smoothing some bias corrected extreme values of the point process. We show how the smoothing permits to obtain Gaussian asymptotic limits and therefore pointwise confidence intervals. Some unidimensional and multidimensional examples are provided. ...

Goodness of fit test for isotonic regression

Cécile Durot, Anne-Sophie Tocquet (2001)

ESAIM: Probability and Statistics

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We consider the problem of hypothesis testing within a monotone regression model. We propose a new test of the hypothesis $H_{0}$ : “ $f = f_{0}$ ” against the composite alternative $H_{a}$ : “ $f \neq f_{0}$ ” under the assumption that the true regression function $f$ is decreasing. The test statistic is based on the $𝕃_{1}$ -distance between the isotonic estimator of $f$ and the function $f_{0}$ , since it is known that a properly centered and normalized version of this distance is asymptotically standard normally distributed under $H_{0}$ . We study...

On pointwise adaptive curve estimation based on inhomogeneous data

Stéphane Gaïffas (2007)

ESAIM: Probability and Statistics

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We want to recover a signal based on noisy inhomogeneous data (the amount of data can vary strongly on the estimation domain). We model the data using nonparametric regression with random design, and we focus on the estimation of the regression at a fixed point with little, or much data. We propose a method which adapts both to the local amount of data (the design density is unknown) and to the local smoothness of the regression function. The procedure consists ...

Diffusions with measurement errors. I. Local asymptotic normality

Arnaud Gloter, Jean Jacod (2001)

ESAIM: Probability and Statistics

Similarity:

We consider a diffusion process $X$ which is observed at times $i / n$ for $i = 0, 1, ..., n$ , each observation being subject to a measurement error. All errors are independent and centered gaussian with known variance $ρ_{n}$ . There is an unknown parameter within the diffusion coefficient, to be estimated. In this first paper the case when $X$ is indeed a gaussian martingale is examined: we can prove that the LAN property holds under quite weak smoothness assumptions, with an explicit limiting Fisher information. What...

Bootstrapping the shorth for regression

Cécile Durot, Karelle Thiébot (2006)

ESAIM: Probability and Statistics

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The paper is concerned with the asymptotic distributions of estimators for the length and the centre of the so-called -shorth interval in a nonparametric regression framework. It is shown that the estimator of the length converges at the -rate to a Gaussian law and that the estimator of the centre converges at the -rate to the location of the maximum of a Brownian motion with parabolic drift. Bootstrap procedures are proposed and shown to be consistent....