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Partition-based conditional density estimation

S. X. Cohen, E. Le Pennec (2013)

ESAIM: Probability and Statistics

We propose a general partition-based strategy to estimate conditional density with candidate densities that are piecewise constant with respect to the covariate. Capitalizing on a general penalized maximum likelihood model selection result, we prove, on two specific examples, that the penalty of each model can be chosen roughly proportional to its dimension. We first study a classical strategy in which the densities are chosen piecewise conditional according to the variable. We then consider Gaussian...

Penalized estimators for non linear inverse problems

Jean-Michel Loubes, Carenne Ludeña (2010)

ESAIM: Probability and Statistics

In this article we tackle the problem of inverse non linear ill-posed problems from a statistical point of view. We discuss the problem of estimating an indirectly observed function, without prior knowledge of its regularity, based on noisy observations. For this we consider two approaches: one based on the Tikhonov regularization procedure, and another one based on model selection methods for both ordered and non ordered subsets. In each case we prove consistency of the estimators and show...

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

Anton Schick, Wolfgang Wefelmeyer (2009)

ESAIM: Probability and Statistics

In this paper we obtain root-n consistency and functional central limit theorems in weighted L1-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 kernel estimator....

Poisson sampling for spectral estimation in periodically correlated processes

Vincent Monsan (1994)

Applicationes Mathematicae

We study estimation problems for periodically correlated, non gaussian processes. We estimate the correlation functions and the spectral densities from continuous-time samples. From a random time sample, we construct three types of estimators for the spectral densities and we prove their consistency.

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