1. Multivariate wavelet estimators for weakly dependent processes: strong consistency rate.
- Author
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Allaoui, Soumaya, Bouzebda, Salim, and Liu, Jicheng
- Subjects
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DENSITY - Abstract
The present article focuses on the non parametric estimation of multivariate density and regression functions. We consider the non parametric linear wavelet-based estimators and investigate the strong consistency from the theoretical viewpoint. In particular, we prove the strong uniform consistency properties of these estimators, over compact subsets of R d , with the determination of the corresponding rates of convergence. As a main contribution, we relax some standard dependence conditions by considering the general concept of the causal α ˜ -weak dependence, including mixing concepts and adapted to diverse classes of interesting statistical processes, essentially the general Bernoulli shifts and the Markov sequences. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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