Debiasing Continuous-time Nonlinear Autoregressions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909570009399296 |
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| author | Kuang, Simon Lin, Xinfan |
| author_facet | Kuang, Simon Lin, Xinfan |
| contents | We study how to identify a class of continuous-time nonlinear systems defined by an ordinary differential equation affine in the unknown parameter. We define a notion of asymptotic consistency as $(n, h) \to (\infty, 0)$, and we achieve it using a family of direct methods where the first step is differentiating a noisy time series and the second step is a plug-in linear estimator. The first step, differentiation, is a signal processing adaptation of the nonparametric statistical technique of local polynomial regression. The second step, generalized linear regression, can be consistent using a least squares estimator, but we demonstrate two novel bias corrections that improve the accuracy for finite $h$. These methods significantly broaden the class of continuous-time systems that can be consistently estimated by direct methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05525 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Debiasing Continuous-time Nonlinear Autoregressions Kuang, Simon Lin, Xinfan Systems and Control Statistics Theory We study how to identify a class of continuous-time nonlinear systems defined by an ordinary differential equation affine in the unknown parameter. We define a notion of asymptotic consistency as $(n, h) \to (\infty, 0)$, and we achieve it using a family of direct methods where the first step is differentiating a noisy time series and the second step is a plug-in linear estimator. The first step, differentiation, is a signal processing adaptation of the nonparametric statistical technique of local polynomial regression. The second step, generalized linear regression, can be consistent using a least squares estimator, but we demonstrate two novel bias corrections that improve the accuracy for finite $h$. These methods significantly broaden the class of continuous-time systems that can be consistently estimated by direct methods. |
| title | Debiasing Continuous-time Nonlinear Autoregressions |
| topic | Systems and Control Statistics Theory |
| url | https://arxiv.org/abs/2504.05525 |