26,539 research outputs found
Convergence rates for density estimators of weakly dependent time series
Assuming that is a vector valued time series with a common
marginal distribution admitting a density , our aim is to provide a wide
range of consistent estimators of . We consider different methods of
estimation of the density as kernel, projection or wavelets ones. Various cases
of weakly dependent series are investigated including the Doukhan & Louhichi
(1999)'s -weak dependence condition, and the -dependence of
Dedecker & Prieur (2005). We thus obtain results for Markov chains, dynamical
systems, bilinear models, non causal Moving Average... From a moment inequality
of Doukhan & Louhichi (1999), we provide convergence rates of the term of error
for the estimation with the \L^q loss or almost surely, uniformly on compact
subsets
Exponential inequalities and functional estimations for weak dependent datas ; applications to dynamical systems
We estimate density and regression functions for weak dependant datas. Using
an exponential inequality obtained by Dedecker and Prieur and in a previous
article of the author, we control the deviation between the estimator and the
function itself. These results are applied to a large class of dynamical
systems and lead to estimations of invariant densities and on the mapping
itself
Adaptive density estimation under dependence
Assume that is a real valued time series admitting a common
marginal density with respect to Lebesgue's measure. Donoho {\it et al.}
(1996) propose a near-minimax method based on thresholding wavelets to estimate
on a compact set in an independent and identically distributed setting. The
aim of the present work is to extend these results to general weak dependent
contexts. Weak dependence assumptions are expressed as decreasing bounds of
covariance terms and are detailed for different examples. The threshold levels
in estimators depend on weak dependence properties of the
sequence through the constant. If these properties are
unknown, we propose cross-validation procedures to get new estimators. These
procedures are illustrated via simulations of dynamical systems and non causal
infinite moving averages. We also discuss the efficiency of our estimators with
respect to the decrease of covariances bounds
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