Mathematics – Statistics Theory
Scientific paper
2006-06-07
Mathematics
Statistics Theory
Scientific paper
In the convolution model $Z\_i=X\_i+ \epsilon\_i$, we give a model selection procedure to estimate the density of the unobserved variables $(X\_i)\_{1 \leq i \leq n}$, when the sequence $(X\_i)\_{i \geq 1}$ is strictly stationary but not necessarily independent. This procedure depends on wether the density of $\epsilon\_i$ is super smooth or ordinary smooth. The rates of convergence of the penalized contrast estimators are the same as in the independent framework, and are minimax over most classes of regularity on ${\mathbb R}$. Our results apply to mixing sequences, but also to many other dependent sequences. When the errors are super smooth, the condition on the dependence coefficients is the minimal condition of that type ensuring that the sequence $(X\_i)\_{i \geq 1}$ is not a long-memory process.
Comte Fabienne
Dedecker Jérôme
Taupin Marie-Luce
No associations
LandOfFree
Adaptive density deconvolution with dependent inputs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Adaptive density deconvolution with dependent inputs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Adaptive density deconvolution with dependent inputs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-698443