Uniform almost sure convergence and asymptotic distribution of the wavelet-based estimators of partial derivatives of multivariate density function under weak dependence. Issue 2 (3rd April 2021)

• Record Type: Journal Article
• Authors: Allaoui, Soumaya; Bouzebda, Salim; Chesneau, Christophe; Liu, Jicheng
• Is Part Of: Journal of nonparametric statistics. Volume 33:Issue 2(2021)
• Page Start: 170
• Page End: 196
• Publication Date: 2021-04-03
• Subjects: Multivariate density estimation -- weakly dependent processes -- stationarity -- wavelets basis; 62E20 -- 62G09; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2021.1925668
• Languages: English
• ISSNs: 1048-5252

Abstract

Abstract : This paper is devoted to the estimation of partial derivatives of multivariate density functions. In this regard, nonparametric linear wavelet-based estimators are introduced, showing their attractive properties from the theoretical point of view. In particular, we prove the strong uniform consistency properties of these estimators, over compact subsets of R d, with the determination of the corresponding convergence rates. Then, we establish the asymptotic normality of these estimators. As a main contribution, we relax some standard dependence conditions; our results hold under a weak dependence condition allowing the consideration of mixing, association, Gaussian sequences and Bernoulli shifts.