Asymptotic estimation for statistical models of continuous-time discrete martingales
The paper deals with statistical experiments of the continuous-time discrete local martingales, including models of all types of point processes. The process of local density of the discrete local martingales is expressed by a stochastic exponent of the stochastic integral according to the compensa...
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Vilnius University Press
2024-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
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| Online Access: | https://ojs.test/index.php/LMR/article/view/37772 |
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| author | Vaidotas Kanišauskas Karolina Kanišauskienė |
| author_facet | Vaidotas Kanišauskas Karolina Kanišauskienė |
| author_sort | Vaidotas Kanišauskas |
| collection | DOAJ |
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The paper deals with statistical experiments of the continuous-time discrete local martingales, including models of all types of point processes. The process of local density of the discrete local martingales is expressed by a stochastic exponent of the stochastic integral according to the compensated point measure. General conditions convenient for testing are determined to assure continuous validity of the maximum probability and Bayesian estimators, as well as the continuous asymptotic normality and the asymptotic minimaxity in each compact of the parametric set. The research applies the optimum Fréchet differentiation of random and parametric functions based on the probability in normed spaces in terms of a continuous compensator. It is demonstrated how the basic conditions become much simpler in the case of the renewal process with the continuous compensator.
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| format | Article |
| id | doaj-art-ccd25a34fbde4d2183b179ea7cefec9a |
| institution | DOAJ |
| issn | 0132-2818 2335-898X |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj-art-ccd25a34fbde4d2183b179ea7cefec9a2025-08-20T02:44:09ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2024-12-0165B10.15388/LMD.2024.37772Asymptotic estimation for statistical models of continuous-time discrete martingalesVaidotas Kanišauskas0https://orcid.org/0000-0002-6097-4080Karolina Kanišauskienė1https://orcid.org/0000-0001-5371-3408Šiauliai Academy, Vilnius UniversityŠiauliai Academy, Vilnius University The paper deals with statistical experiments of the continuous-time discrete local martingales, including models of all types of point processes. The process of local density of the discrete local martingales is expressed by a stochastic exponent of the stochastic integral according to the compensated point measure. General conditions convenient for testing are determined to assure continuous validity of the maximum probability and Bayesian estimators, as well as the continuous asymptotic normality and the asymptotic minimaxity in each compact of the parametric set. The research applies the optimum Fréchet differentiation of random and parametric functions based on the probability in normed spaces in terms of a continuous compensator. It is demonstrated how the basic conditions become much simpler in the case of the renewal process with the continuous compensator. https://ojs.test/index.php/LMR/article/view/37772continuous-time discrete local martingalelocal asymptotic normalitycompensatordifferentiation in normed spaces |
| spellingShingle | Vaidotas Kanišauskas Karolina Kanišauskienė Asymptotic estimation for statistical models of continuous-time discrete martingales Lietuvos Matematikos Rinkinys continuous-time discrete local martingale local asymptotic normality compensator differentiation in normed spaces |
| title | Asymptotic estimation for statistical models of continuous-time discrete martingales |
| title_full | Asymptotic estimation for statistical models of continuous-time discrete martingales |
| title_fullStr | Asymptotic estimation for statistical models of continuous-time discrete martingales |
| title_full_unstemmed | Asymptotic estimation for statistical models of continuous-time discrete martingales |
| title_short | Asymptotic estimation for statistical models of continuous-time discrete martingales |
| title_sort | asymptotic estimation for statistical models of continuous time discrete martingales |
| topic | continuous-time discrete local martingale local asymptotic normality compensator differentiation in normed spaces |
| url | https://ojs.test/index.php/LMR/article/view/37772 |
| work_keys_str_mv | AT vaidotaskanisauskas asymptoticestimationforstatisticalmodelsofcontinuoustimediscretemartingales AT karolinakanisauskiene asymptoticestimationforstatisticalmodelsofcontinuoustimediscretemartingales |