A Robbins-Monro algorithm for non-parametric estimation of NAR process with Markov-Switching: asymptotic normality
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arXiv
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| Natura: | Preprint |
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2026
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| _version_ | 1866908924726214656 |
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| author | Fermin, Lisandro Rios, Ricardo Rodríguez, Luis-Ángel |
| author_facet | Fermin, Lisandro Rios, Ricardo Rodríguez, Luis-Ángel |
| contents | This paper is the second part of our study on the non-parametric estimation of MS-NAR processes started with [L. Fermin et al. 2017]. We consider the Nadaraya-Watson type regression function estimator for non-linear autoregressive Markov switching processes. In this context the regression function estimator is interpreted as a solution of a local weighted We have introduced, in the first work, a restoration-estimation Robbins-Monro algorithm to approximate the estimator, and we proved identifiability of model and the consistency of the non-parametric estimator. In this work, we obtain the central limit theorem for the non-parametric estimator, whether the Markov chain is observed or not. Finally, we present a detailed simulation study illustrating the performances of our estimation procedure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29440 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Robbins-Monro algorithm for non-parametric estimation of NAR process with Markov-Switching: asymptotic normality Fermin, Lisandro Rios, Ricardo Rodríguez, Luis-Ángel Methodology This paper is the second part of our study on the non-parametric estimation of MS-NAR processes started with [L. Fermin et al. 2017]. We consider the Nadaraya-Watson type regression function estimator for non-linear autoregressive Markov switching processes. In this context the regression function estimator is interpreted as a solution of a local weighted We have introduced, in the first work, a restoration-estimation Robbins-Monro algorithm to approximate the estimator, and we proved identifiability of model and the consistency of the non-parametric estimator. In this work, we obtain the central limit theorem for the non-parametric estimator, whether the Markov chain is observed or not. Finally, we present a detailed simulation study illustrating the performances of our estimation procedure. |
| title | A Robbins-Monro algorithm for non-parametric estimation of NAR process with Markov-Switching: asymptotic normality |
| topic | Methodology |
| url | https://arxiv.org/abs/2603.29440 |