Abstract
In this paper, we establish a general result on complete moment convergence and the Marcinkiewicz–Zygmund-type strong law of large numbers for weighted sums of m-asymptotic negatively associated random variables, which improve and extend some existing ones. As applications of our main results, we present a result on complete consistency for the weighted estimator in a nonparametric regression model and a result on strong consistency for conditional Value-at-risk estimator based on m-asymptotic negatively associated errors. We also carry out some numerical simulations to confirm the theoretical results.
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The authors are most grateful to the Editor and anonymous referee for carefully reading the manuscript and valuable suggestions which helped in improving an earlier version of this paper.
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Supported by the National Natural Science Foundation of China (Grant Nos. 11671012, 11871072), the Natural Science Foundation of Anhui Province (Grant No. 1908085QA01), the Provincial Natural Science Research Project of Anhui Colleges (Grant No. KJ2019A0003) and the Project on Reserve Candidates for Academic and Technical Leaders of Anhui Province (Grant No. 2017H123)
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Wu, Y., Wang, X. & Shen, A. Strong convergence properties for weighted sums of m-asymptotic negatively associated random variables and statistical applications. Stat Papers 62, 2169–2194 (2021). https://doi.org/10.1007/s00362-020-01179-z
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DOI: https://doi.org/10.1007/s00362-020-01179-z
Keywords
- m-Asymptotic negatively associated random variables
- Complete moment convergence
- Complete convergence
- Strong law of large numbers
- Nonparametric regression model
- Conditional value-at-risk
- Complete consistency
- Strong consistency