Abstract
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.
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Acknowledgements
The authors are most grateful to the Editor and anonymous referees for carefully reading the manuscript and for valuable suggestions which helped to improve an earlier version of this paper. This work was supported by the National Natural Science Foundation of China (11671012), the Natural Science Foundation of Anhui Province (1508085J06), the Key Projects for Academic Talent of Anhui Province (gxbjZD2016005) and the Students Innovative Training Project of Anhui University (201710357185).
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Xi, M., Wang, R., Cheng, Z. et al. Some convergence properties for partial sums of widely orthant dependent random variables and their statistical applications. Stat Papers 61, 1663–1684 (2020). https://doi.org/10.1007/s00362-018-0996-y
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DOI: https://doi.org/10.1007/s00362-018-0996-y
Keywords
- Widely orthant dependent random variables
- Cesàro uniform integrability
- Complete convergence
- Complete consistency
- Nonparametric regression model