Convergence rates for density estimators of weakly dependent time series

Details Convergence rates for density estimators of weakly dependent time series Convergence rates for density estimators of weakly dependent time series

2006-03-10

arxiv.org/abs/math/0603254v2

Dependence in Probability and Statistics. Springer (Ed.) (2006) 380

Mathematics

Statistics Theory

Scientific paper

Assuming that $(X_t)_{t\in\Z}$ is a vector valued time series with a common marginal distribution admitting a density $f$, our aim is to provide a wide range of consistent estimators of $f$. 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 $\eta$-weak dependence condition, and the $\tilde \phi$-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.

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