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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...
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...
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....
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.
Dvoretzky-Kiefer-Wolfowitz type inequalities for some polynomial and spline estimators of distribution functions are constructed. Moreover, hints on the corresponding algorithms are given as well.
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