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Multivariate wavelet density and regression estimators for stationary and ergodic discrete time processes: asymptotic results. (English) Zbl 1360.62155

Summary: In the present paper, we are mainly concerned with the non parametric estimation of the density as well as the regression function by using orthonormal wavelet bases. We provide the strong uniform consistency properties with rates of these estimators, over compact subsets of \(\mathbb R^d\), under a general ergodic condition on the underlying processes. We characterize the asymptotic normality of considered wavelet-based estimators, under easily verifiable conditions. The asymptotic properties of these estimators are obtained, by means of the martingale approach.

MSC:

62G07 Density estimation
62G08 Nonparametric regression and quantile regression
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62H05 Characterization and structure theory for multivariate probability distributions; copulas
60G42 Martingales with discrete parameter
60G46 Martingales and classical analysis
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