Bulletin of the
Korean Mathematical Society BKMS

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)