Complete f -moment convergence for sums of asymptotically almost negatively associated random variables with statistical applications

Abstract

AbstractIn this paper, we mainly study the complete f-moment convergence for sums of asymptotically almost negatively associated (AANA, for short) random variables and provide an application. A general result on complete f-moment convergence for arrays of rowwise AANA random variables is obtained. We also give an application to nonparametric regression models based on AANA errors by using the result on complete f-moment convergence that we have established. A sufficient and necessary moment condition for the complete consistency is presented. Finally, a numerical simulation is provided to verify the validity of the theoretical result.Keywords: Asymptotically almost negatively associated random variablescomplete f-moment convergencecomplete convergencenonparametric regression modelcomplete consistencyMathematical subject classifications: 60F1562G05 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 author(s).Additional informationFundingSupported by the National Social Science Foundation of China (22BTJ059).