2006/06/07 by Fabienne Comte, Comte, Fabienne, Jérôme Dedecker +3
Computer Science · Economics, Econometrics and Finance · Mathematics · #62G07-62G20 #Bayesian Methods and Mixture Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.math/0606166
openalex publication_date 2006/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the convolution model Z_i=X_i+ ε_i, we give a model selection procedure to estimate the density of the unobserved variables (X_i)_1 ≤ i ≤ n, when the sequence (X_i)_i ≥ 1 is strictly stationary but not necessarily independent. This procedure depends on wether the density of ε_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 ≥ 1 is not a long-memory process.