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Some convergence properties for partial sums of widely orthant dependent random variables and their statistical applications. (English) Zbl 07268974
Summary: In this paper, we present the \(L_p\) convergence for partial sums \(S_n=\sum_{k=1}^nX_k\) under the Cesàro uniform integrability condition and the complete convergence for the maximum of \(S_n\) for sequences of widely orthant dependent random variables \(\{X_n,n\ge 1\}.\) Some of the results extend the corresponding ones in reference. As applications, we get the complete consistency and the strong consistency for the estimator in a nonparametric regression model.
MSC:
60F15 Strong limit theorems
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
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