Some convergence properties for arrays of rowwise asymptotically almost negatively associated random variables under sub-linear expectations
In this article, under some suitable conditions, we study the L q convergence and complete q-th moment convergence for arrays of rowwise asymptotically almost negatively associated (AANA, for short) random variables under sub-linear expectations. Some general results on L q convergence and complete...
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| Published in | Stochastic models Vol. 40; no. 3; pp. 536 - 568 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Taylor & Francis
02.07.2024
Taylor & Francis Ltd |
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| Abstract | In this article, under some suitable conditions, we study the L
q
convergence and complete q-th moment convergence for arrays of rowwise asymptotically almost negatively associated (AANA, for short) random variables under sub-linear expectations. Some general results on L
q
convergence and complete q-th moment convergence for arrays of rowwise AANA random variables under sub-linear expectations are established, which extend the corresponding ones from classic probability space to the case of sub-linear expectation space. As applications of our main results, we not only present a result on the complete consistency of the weighted estimator in a nonparametric regression model but also obtain the complete consistency of the estimators in errors-in-variables (EV, for short) regression models based on AANA errors under sub-linear expectations. We perform some numerical simulations to verify the validity of the theoretical results. |
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| AbstractList | In this article, under some suitable conditions, we study the L
q
convergence and complete q-th moment convergence for arrays of rowwise asymptotically almost negatively associated (AANA, for short) random variables under sub-linear expectations. Some general results on L
q
convergence and complete q-th moment convergence for arrays of rowwise AANA random variables under sub-linear expectations are established, which extend the corresponding ones from classic probability space to the case of sub-linear expectation space. As applications of our main results, we not only present a result on the complete consistency of the weighted estimator in a nonparametric regression model but also obtain the complete consistency of the estimators in errors-in-variables (EV, for short) regression models based on AANA errors under sub-linear expectations. We perform some numerical simulations to verify the validity of the theoretical results. In this article, under some suitable conditions, we study the Lq convergence and complete q-th moment convergence for arrays of rowwise asymptotically almost negatively associated (AANA, for short) random variables under sub-linear expectations. Some general results on Lq convergence and complete q-th moment convergence for arrays of rowwise AANA random variables under sub-linear expectations are established, which extend the corresponding ones from classic probability space to the case of sub-linear expectation space. As applications of our main results, we not only present a result on the complete consistency of the weighted estimator in a nonparametric regression model but also obtain the complete consistency of the estimators in errors-in-variables (EV, for short) regression models based on AANA errors under sub-linear expectations. We perform some numerical simulations to verify the validity of the theoretical results. |
| Author | Zheng, Shunping Wang, Miaomiao Wang, Xuejun |
| Author_xml | – sequence: 1 givenname: Miaomiao surname: Wang fullname: Wang, Miaomiao organization: School of Big Data and Statistics, Anhui University – sequence: 2 givenname: Shunping surname: Zheng fullname: Zheng, Shunping organization: School of Big Data and Statistics, Anhui University – sequence: 3 givenname: Xuejun surname: Wang fullname: Wang, Xuejun organization: School of Big Data and Statistics, Anhui University |
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| Snippet | In this article, under some suitable conditions, we study the L
q
convergence and complete q-th moment convergence for arrays of rowwise asymptotically almost... In this article, under some suitable conditions, we study the Lq convergence and complete q-th moment convergence for arrays of rowwise asymptotically almost... |
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| SubjectTerms | Arrays Asymptotically almost negatively associated random variables capacity complete moment convergence Consistency Convergence Errors Numerical models Random variables Regression models Statistical analysis sub-linear expectation space |
| Title | Some convergence properties for arrays of rowwise asymptotically almost negatively associated random variables under sub-linear expectations |
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