Complete f -moment convergence for a class of random variables with related statistical applications

Abstract

Abstract.In this article, we establish the complete f-moment convergence for a class of random variables satisfying a Rosenthal-type maximal inequality and a weak mean dominating condition with a mean dominating variable. As corollaries, the complete moment convergence and complete convergence for a class of random variables are also obtained. In addition, an application of main results to nonparametric regression models is provided. Finally, we provide a numerical simulation to verify the validity of our theoretical results based on finite samples.Keywords: Complete consistencycomplete f-moment convergencenonparametric regression modelsRosenthal-type maximal inequalityMSC:: 60F1562G20 AcknowledgmentsThe authors are most grateful to the Editor and anonymous referee for carefully reading the manuscript and valuable suggestions which helped in improving an earlier version of this paper.Disclosure statementNo potential conflict of interest was reported by the authors.Additional informationFunding Supported by the National Social Science Foundation of China (22BTJ059).