Abstract
In this paper, we establish the complete convergence of the weighted sums for martingale differences, which is the interesting supplements for some known results. As statistical applications, when errors are martingale differences, the least square estimator in the errors-in-variables regression model and the regression function estimator in nonparametric regression model are studied and their strong consistency is obtained.
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Communicated by Anton Abdulbasah Kamil.
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Miao, Y., Shao, M. Complete Convergence of Weighted Sums of Martingale Differences and Statistical Applications. Bull. Malays. Math. Sci. Soc. 46, 116 (2023). https://doi.org/10.1007/s40840-023-01515-0
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DOI: https://doi.org/10.1007/s40840-023-01515-0
Keywords
- Complete convergence
- Martingale difference
- Errors-in-variables regression model
- Least square estimator
- Regression function estimator
- Regression model
- Strong consistency