Parameter Estimation of Linear Stochastic Differential Equations with Sparse Observations
We consider parameter estimation for linear stochastic differential equations with independent experiments observed at infrequent and irregularly spaced follow-up times. The maximum likelihood method is used to obtain an asymptotically consistent estimator. A kernel-weighted score function is propos...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/14/12/2500 |
| _version_ | 1797455168978026496 |
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| author | Yuecai Han Zhe Yin Dingwen Zhang |
| author_facet | Yuecai Han Zhe Yin Dingwen Zhang |
| author_sort | Yuecai Han |
| collection | DOAJ |
| description | We consider parameter estimation for linear stochastic differential equations with independent experiments observed at infrequent and irregularly spaced follow-up times. The maximum likelihood method is used to obtain an asymptotically consistent estimator. A kernel-weighted score function is proposed for the parameter in drift terms. The strong consistency and the rate of convergence of the estimator are obtained. The numerical results show that the proposed estimator performs well with moderate sample sizes. |
| first_indexed | 2024-03-09T15:48:37Z |
| format | Article |
| id | doaj.art-5e34c01e51a0493190ed7b6b6fa3c81f |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T15:48:37Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-5e34c01e51a0493190ed7b6b6fa3c81f2023-11-24T18:18:50ZengMDPI AGSymmetry2073-89942022-11-011412250010.3390/sym14122500Parameter Estimation of Linear Stochastic Differential Equations with Sparse ObservationsYuecai Han0Zhe Yin1Dingwen Zhang2School of Mathematics, Jilin University, Changchun 130012, ChinaSchool of Mathematics, Jilin University, Changchun 130012, ChinaSchool of Mathematics, Jilin University, Changchun 130012, ChinaWe consider parameter estimation for linear stochastic differential equations with independent experiments observed at infrequent and irregularly spaced follow-up times. The maximum likelihood method is used to obtain an asymptotically consistent estimator. A kernel-weighted score function is proposed for the parameter in drift terms. The strong consistency and the rate of convergence of the estimator are obtained. The numerical results show that the proposed estimator performs well with moderate sample sizes.https://www.mdpi.com/2073-8994/14/12/2500kernel-weighted estimationlinear stochastic differential equationsgeometric Brownian motionlikelihood function |
| spellingShingle | Yuecai Han Zhe Yin Dingwen Zhang Parameter Estimation of Linear Stochastic Differential Equations with Sparse Observations Symmetry kernel-weighted estimation linear stochastic differential equations geometric Brownian motion likelihood function |
| title | Parameter Estimation of Linear Stochastic Differential Equations with Sparse Observations |
| title_full | Parameter Estimation of Linear Stochastic Differential Equations with Sparse Observations |
| title_fullStr | Parameter Estimation of Linear Stochastic Differential Equations with Sparse Observations |
| title_full_unstemmed | Parameter Estimation of Linear Stochastic Differential Equations with Sparse Observations |
| title_short | Parameter Estimation of Linear Stochastic Differential Equations with Sparse Observations |
| title_sort | parameter estimation of linear stochastic differential equations with sparse observations |
| topic | kernel-weighted estimation linear stochastic differential equations geometric Brownian motion likelihood function |
| url | https://www.mdpi.com/2073-8994/14/12/2500 |
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