Invariance Principle and Berry–Esseen Bound for Error Variance Estimator for Pth-Order Nonlinear Autoregressive Models
The invariance principle and Berry–Esseen bound for an error variance estimator based on the residuals are established by using a Taylor expansion and the classical invariance principle and Berry–Esseen bound for independent random variables. Some examples are given to illustrate their applications....
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MDPI AG
2024-10-01
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| author | Kaiyu Liang Yong Zhang Xue Ding |
| author_facet | Kaiyu Liang Yong Zhang Xue Ding |
| author_sort | Kaiyu Liang |
| collection | DOAJ |
| description | The invariance principle and Berry–Esseen bound for an error variance estimator based on the residuals are established by using a Taylor expansion and the classical invariance principle and Berry–Esseen bound for independent random variables. Some examples are given to illustrate their applications. |
| format | Article |
| id | doaj-art-2e651d16038547bf872f53e0f91799c0 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-2e651d16038547bf872f53e0f91799c02024-11-26T17:50:46ZengMDPI AGAxioms2075-16802024-10-01131174610.3390/axioms13110746Invariance Principle and Berry–Esseen Bound for Error Variance Estimator for Pth-Order Nonlinear Autoregressive ModelsKaiyu Liang0Yong Zhang1Xue Ding2School of Mathematics, Jilin University, Changchun 130012, ChinaSchool of Mathematics, Jilin University, Changchun 130012, ChinaSchool of Mathematics, Jilin University, Changchun 130012, ChinaThe invariance principle and Berry–Esseen bound for an error variance estimator based on the residuals are established by using a Taylor expansion and the classical invariance principle and Berry–Esseen bound for independent random variables. Some examples are given to illustrate their applications.https://www.mdpi.com/2075-1680/13/11/746nonlinear autoregressive modelsinvariance principleBerry–Esseen bounderror variance estimatorresiduals |
| spellingShingle | Kaiyu Liang Yong Zhang Xue Ding Invariance Principle and Berry–Esseen Bound for Error Variance Estimator for Pth-Order Nonlinear Autoregressive Models Axioms nonlinear autoregressive models invariance principle Berry–Esseen bound error variance estimator residuals |
| title | Invariance Principle and Berry–Esseen Bound for Error Variance Estimator for Pth-Order Nonlinear Autoregressive Models |
| title_full | Invariance Principle and Berry–Esseen Bound for Error Variance Estimator for Pth-Order Nonlinear Autoregressive Models |
| title_fullStr | Invariance Principle and Berry–Esseen Bound for Error Variance Estimator for Pth-Order Nonlinear Autoregressive Models |
| title_full_unstemmed | Invariance Principle and Berry–Esseen Bound for Error Variance Estimator for Pth-Order Nonlinear Autoregressive Models |
| title_short | Invariance Principle and Berry–Esseen Bound for Error Variance Estimator for Pth-Order Nonlinear Autoregressive Models |
| title_sort | invariance principle and berry esseen bound for error variance estimator for pth order nonlinear autoregressive models |
| topic | nonlinear autoregressive models invariance principle Berry–Esseen bound error variance estimator residuals |
| url | https://www.mdpi.com/2075-1680/13/11/746 |
| work_keys_str_mv | AT kaiyuliang invarianceprincipleandberryesseenboundforerrorvarianceestimatorforpthordernonlinearautoregressivemodels AT yongzhang invarianceprincipleandberryesseenboundforerrorvarianceestimatorforpthordernonlinearautoregressivemodels AT xueding invarianceprincipleandberryesseenboundforerrorvarianceestimatorforpthordernonlinearautoregressivemodels |