Convergence properties for the partial sums of widely orthant dependent random variables under some integrable assumptions and their applications
Bull. Korean Math. Soc. 2020 Vol. 57, No. 6, 1451-1473
Published online September 11, 2020
Printed November 30, 2020
Yongping He, Xuejun Wang, Chi Yao
Anhui University; Anhui University; Anhui University
Abstract : Widely orthant dependence (WOD, in short) is a special dependence structure. In this paper, by using the probability inequalities and moment inequalities for WOD random variables, we study the $L_p$ convergence and complete convergence for the partial sums respectively under the conditions of RCI$(\alpha)$, SRCI$(\alpha)$ and $R$-$h$-integrability. We also give an application to nonparametric regression models based on WOD errors by using the $L_p$ convergence that we obtained. Finally we carry out some simulations to verify the validity of our theoretical results.
Keywords : Widely orthant dependent random variables, $L_p$ convergence, complete convergence, residual Ces\`{a}ro alpha-integrability, strongly residual Ces\`{a}ro alpha integrability, $R$-$h$-integrability
MSC numbers : 60F05, 60F15, 60F25, 62G05
Supported by : Supported by the National Natural Science Foundation of China (11671012, 11871072, 11701004, 11701005), the Natural Science Foundation of Anhui Province (1808085QA03, 1908085QA01, 1908085QA07), the Provincial Natural Science Research Project of Anhui Colleges (KJ2019A0003) and the Project on Reserve Candidates for Academic and Technical Leaders of Anhui Province (2017H123)
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