Multivariate wavelet density and regression estimators for stationary and ergodic discrete time processes: Asymptotic results

Salim Bouzebda and Sultana Didi

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 3, 1367-1406

Abstract: 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 Rd$\mathbb {R}^{d}$, 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.

Date: 2017
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:taf:lstaxx:v:46:y:2017:i:3:p:1367-1406

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DOI: 10.1080/03610926.2015.1019144

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