Displaying similar documents to “Density deconvolution with associated stationary data”

Asymptotic normality of the integrated square error of a density estimator in the convolution model.

Cristina Butucea (2004)

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In this paper we consider a kernel estimator of a density in a convolution model and give a central limit theorem for its integrated square error (ISE). The kernel estimator is rather classical in minimax theory when the underlying density is recovered from noisy observations. The kernel is fixed and depends heavily on the distribution of the noise, supposed entirely known. The bandwidth is not fixed, the results hold for any sequence of bandwidths decreasing to 0. In particular the...

Plug-in estimators for higher-order transition densities in autoregression

Anton Schick, Wolfgang Wefelmeyer (2009)

ESAIM: Probability and Statistics

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In this paper we obtain root- consistency and functional central limit theorems in weighted -spaces for plug-in estimators of the two-step transition density in the classical stationary linear autoregressive model of order one, assuming essentially only that the innovation density has bounded variation. We also show that plugging in a properly weighted residual-based kernel estimator for the unknown innovation density improves on plugging in an unweighted residual-based...

Minimax and bayes estimation in deconvolution problem

Mikhail Ermakov (2008)

ESAIM: Probability and Statistics

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We consider a deconvolution problem of estimating a signal blurred with a random noise. The noise is assumed to be a stationary Gaussian process multiplied by a weight function function where and is a small parameter. The underlying solution is assumed to be infinitely differentiable. For this model we find asymptotically minimax and Bayes estimators. In the case of solutions having finite number of derivatives similar results were obtained in [G.K. Golubev and R.Z. Khasminskii,...

Asymptotic unbiased density estimators

Nicolas W. Hengartner, Éric Matzner-Løber (2009)

ESAIM: Probability and Statistics

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This paper introduces a computationally tractable density estimator that has the same asymptotic variance as the classical Nadaraya-Watson density estimator but whose asymptotic bias is zero. We achieve this result using a two stage estimator that applies a multiplicative bias correction to an oversmooth pilot estimator. Simulations show that our asymptotic results are available for samples as low as , where we see an improvement of as much as 20% over the traditionnal estimator. ...

Mean square error of the estimator of the conditional hazard function

Abbes Rabhi, Samir Benaissa, El Hadj Hamel, Boubaker Mechab (2013)

Applicationes Mathematicae

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This paper deals with a scalar response conditioned by a functional random variable. The main goal is to estimate the conditional hazard function. An asymptotic formula for the mean square error of this estimator is calculated considering as usual the bias and variance.

Changepoint estimation for dependent and non-stationary panels

Michal Pešta, Barbora Peštová, Matúš Maciak (2020)

Applications of Mathematics

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The changepoint estimation problem of a common change in panel means for a very general panel data structure is considered. The observations within each panel are allowed to be generally dependent and non-stationary. Simultaneously, the panels are weakly dependent and non-stationary among each other. The follow up period can be extremely short and the changepoint magnitudes may differ across the panels accounting also for a specific situation that some magnitudes are equal to zero (thus,...

Large and Moderate Deviations Principles for Recursive Kernel Estimator of a Multivariate Density and its Partial Derivatives

Mokkadem, Abdelkader, Mariane, Pelletier, Baba, Thiam (2006)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 62G07, 60F10. In this paper we prove large and moderate deviations principles for the recursive kernel estimator of a probability density function and its partial derivatives. Unlike the density estimator, the derivatives estimators exhibit a quadratic behaviour not only for the moderate deviations scale but also for the large deviations one. We provide results both for the pointwise and the uniform deviations.

On invariant density estimation for ergodic diffusion processes.

Yuri A. Kutoyants (2004)

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We present a review of several results concerning invariant density estimation by observations of ergodic diffusion process and some related problems. In every problem we propose a lower minimax bound on the risks of all estimators and then we construct an asymptotically efficient estimator.