Rate of complete second-order moment convergence and theoretical applications. Issue 1 (31st December 2022)

• Record Type: Journal Article
• Authors: Laroussi, I.; Madi, M.
• Is Part Of: Journal of Taibah University for science. Volume 16:Issue 1(2022)
• Page Start: 566
• Page End: 574
• Publication Date: 2022-12-31
• Subjects: Kernel density estimator -- kernel distribution estimator -- kernel quantile estimator -- complete moment convergence -- nonparametric estimation -- rate of convergence -- complete convergence; Science -- Periodicals; Science; Periodicals; 505
• DOI: 10.1080/16583655.2022.2082179
• Languages: English
• ISSNs: 1658-3655

Abstract

ABSTRACT: The purpose of this work is to present a novel mode of convergence, complete second-order moment convergence with rate, which implies almost complete convergence and gives a smaller rate of convergence. Indeed, this mode is easier to obtain and gives better performances than those of the almost complete convergence in the case of the nonparametric estimators with kernels of the density function, of the distribution function and of the quantile function. A great advantage of the proposed approach is that less conditions are imposed to the kernel function thanks to the use of the mean squared error expression.