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Strong Law of Large Numbers for Weighted Sums of Random Variables and Its Applications in EV Regression Models

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Abstract

This paper mainly studies the strong convergence properties for weighted sums of extended negatively dependent (END, for short) random variables. Some sufficient conditions to prove the strong law of large numbers for weighted sums of END random variables are provided. In particular, the authors obtain the weighted version of Kolmogorov type strong law of large numbers for END random variables as a product. The results that the authors obtained generalize the corresponding ones for independent random variables and some dependent random variables. As an application, the authors investigate the errors-in-variables (EV, for short) regression models and establish the strong consistency for the least square estimators. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analysed for illustration.

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Authors and Affiliations

  1. School of Mathematical Sciences, Anhui University, Hefei, 230601, China

    Yunjie Peng, Xiaoqian Zheng, Wei Yu & Xuejun Wang

  2. Wendian College, Anhui University, Hefei, 230601, China

    Kaixin He

Authors
  1. Yunjie Peng
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  2. Xiaoqian Zheng
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  3. Wei Yu
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  4. Kaixin He
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  5. Xuejun Wang
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Corresponding author

Correspondence to Xuejun Wang.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11671012 and 11871072, the Natural Science Foundation of Anhui Province under Grant Nos. 1808085QA03, 1908085QA01, 1908085QA07, the Provincial Natural Science Research Project of Anhui Colleges under Grant No. KJ2019A0003 and the Students Innovative Training Project of Anhui University under Grant No. 201910357002.

This paper was recommended for publication by Editor JIN Baisuo.

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Peng, Y., Zheng, X., Yu, W. et al. Strong Law of Large Numbers for Weighted Sums of Random Variables and Its Applications in EV Regression Models. J Syst Sci Complex 35, 342–360 (2022). https://doi.org/10.1007/s11424-020-0098-5

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  • DOI: https://doi.org/10.1007/s11424-020-0098-5

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