Statistical Estimation and Hypothesis Testing on Impulse Response Function
In this paper a time-invariant continuous linear system is considered with a real-valued impulse response function (IRF) which is defined on a bounded domain. A sample input- output cross-correlogram is taken as an estimator of the response function. The input processes are supposed to be zero-m...
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| Format: | Article |
| Language: | English |
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Austrian Statistical Society
2025-01-01
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| Series: | Austrian Journal of Statistics |
| Online Access: | https://www.ajs.or.at/index.php/ajs/article/view/1977 |
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| author | Iryna Rozora Anastasiia Melnyk |
| author_facet | Iryna Rozora Anastasiia Melnyk |
| author_sort | Iryna Rozora |
| collection | DOAJ |
| description |
In this paper a time-invariant continuous linear system is considered with a real-valued impulse response function (IRF) which is defined on a bounded domain. A sample input- output cross-correlogram is taken as an estimator of the response function. The input processes are supposed to be zero-mean stationary Gaussian process and can be repre- sented as a finite sum with uncorrelated terms. A rate of convergence of IRF estimator in the space L2([0,Λ]) is obtained that gives a possibility to propose a nonparametric goodness-of-fit testing on IRF.
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| format | Article |
| id | doaj-art-4696186a7b8144a7a386ebdf1eb03de3 |
| institution | Kabale University |
| issn | 1026-597X |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Austrian Statistical Society |
| record_format | Article |
| series | Austrian Journal of Statistics |
| spelling | doaj-art-4696186a7b8144a7a386ebdf1eb03de32025-01-13T07:12:21ZengAustrian Statistical SocietyAustrian Journal of Statistics1026-597X2025-01-0154110.17713/ajs.v54i1.1977Statistical Estimation and Hypothesis Testing on Impulse Response FunctionIryna Rozora0Anastasiia Melnyk1Taras Shevchenko NAtional University of KyivTaras Shevchenko National University of Kyiv In this paper a time-invariant continuous linear system is considered with a real-valued impulse response function (IRF) which is defined on a bounded domain. A sample input- output cross-correlogram is taken as an estimator of the response function. The input processes are supposed to be zero-mean stationary Gaussian process and can be repre- sented as a finite sum with uncorrelated terms. A rate of convergence of IRF estimator in the space L2([0,Λ]) is obtained that gives a possibility to propose a nonparametric goodness-of-fit testing on IRF. https://www.ajs.or.at/index.php/ajs/article/view/1977 |
| spellingShingle | Iryna Rozora Anastasiia Melnyk Statistical Estimation and Hypothesis Testing on Impulse Response Function Austrian Journal of Statistics |
| title | Statistical Estimation and Hypothesis Testing on Impulse Response Function |
| title_full | Statistical Estimation and Hypothesis Testing on Impulse Response Function |
| title_fullStr | Statistical Estimation and Hypothesis Testing on Impulse Response Function |
| title_full_unstemmed | Statistical Estimation and Hypothesis Testing on Impulse Response Function |
| title_short | Statistical Estimation and Hypothesis Testing on Impulse Response Function |
| title_sort | statistical estimation and hypothesis testing on impulse response function |
| url | https://www.ajs.or.at/index.php/ajs/article/view/1977 |
| work_keys_str_mv | AT irynarozora statisticalestimationandhypothesistestingonimpulseresponsefunction AT anastasiiamelnyk statisticalestimationandhypothesistestingonimpulseresponsefunction |