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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.
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참고문헌 (31)
참고문헌 신청
Francesca Bruno / 2016 / Non-parametric regression on compositional covariates using Bayesian P-splines / Statistical Methods & Applications 25(1):75~88
T. K. Chandra / 2006 / Cesàro α-Integrability and Laws of Large Numbers-II / Journal of Theoretical Probability 19(4):789~816
Pingyan Chen / 2019 / A Spitzer-type law of large numbers for widely orthant dependent random variables / Statistics & Probability Letters 154:108544
Wei Chen / 2016 / An inequality of widely dependent random variables and its applications* / Lithuanian Mathematical Journal 56(1):16~31
Z. Chen / 2016 / The consistency for the estimator of nonparametric regression model based on martingale difference errors / Statist. Papers 57(2):451~469
T. K. Chandra / 2006 / Cesàro α-Integrability and Laws of Large Numbers-II / Journal of Theoretical Probability 19(4):789~816
Pingyan Chen / 2019 / A Spitzer-type law of large numbers for widely orthant dependent random variables / Statistics & Probability Letters 154:108544
Wei Chen / 2016 / An inequality of widely dependent random variables and its applications* / Lithuanian Mathematical Journal 56(1):16~31
Z. Chen / 2016 / The consistency for the estimator of nonparametric regression model based on martingale difference errors / Statist. Papers 57(2):451~469
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