Multivariate wavelet density estimation for strong mixing stratified size-biased sample

• Published in: Communications in statistics. Theory and methods Vol. 52; no. 6; pp. 1888 - 1904
• Main Authors: Kou, Junke, Cui, Kaili
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 19-03-2023; Taylor & Francis Ltd
• Subjects: Convergence; Density; Function space; mean integrated squared error; Multivariate analysis; Multivariate density estimation; stratified size-biased; strong mixing; Upper bounds; wavelets
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2021.1941111

This paper considers wavelet estimations of a multivariate density function based on stratified size-biased and strong mixing data. We provide upper bounds of the mean integrated squared error for linear and nonlinear wavelet estimators in Besov space
It is shown that the linear estimator achieves the optimal convergence rate in the case of
Moreover, the convergence rate of nonlinear estimator coincides with the optimal convergence rate up to a
factor for
In addition, the nonlinear wavelet estimator is adaptive.