Bias reduction of a conditional maximum likelihood estimator for a Gaussian second-order moving average model
In this study, we consider a bias reduction of the conditional maximum likelihood estimators for the unknown parameters of a Gaussian second-order moving average (MA(2)) model. In many cases, we use the maximum likelihood estimator because the estimator is consistent. However, when the sample size n...
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oai:doaj.org-article:cba596a44dff40e7a745555c81f32b272021-11-17T08:47:28ZBias reduction of a conditional maximum likelihood estimator for a Gaussian second-order moving average model10.15559/21-VMSTA1872351-60462351-6054https://doaj.org/article/cba596a44dff40e7a745555c81f32b272021-08-01T00:00:00Zhttps://www.vmsta.org/doi/10.15559/21-VMSTA187https://doaj.org/toc/2351-6046https://doaj.org/toc/2351-6054In this study, we consider a bias reduction of the conditional maximum likelihood estimators for the unknown parameters of a Gaussian second-order moving average (MA(2)) model. In many cases, we use the maximum likelihood estimator because the estimator is consistent. However, when the sample size n is small, the error is large because it has a bias of $O({n^{-1}})$. Furthermore, the exact form of the maximum likelihood estimator for moving average models is slightly complicated even for Gaussian models. We sometimes rely on simpler maximum likelihood estimation methods. As one of the methods, we focus on the conditional maximum likelihood estimator and examine the bias of the conditional maximum likelihood estimator for a Gaussian MA(2) model. Moreover, we propose new estimators for the unknown parameters of the Gaussian MA(2) model based on the bias of the conditional maximum likelihood estimators. By performing simulations, we investigate properties of this bias, as well as the asymptotic variance of the conditional maximum likelihood estimators for the unknown parameters. Finally, we confirm the validity of the new estimators through this simulation study.Fumiaki HondaTakeshi KurosawaVTeXarticleGaussian second-order moving average modelconditional maximum likelihood estimatorsbias reductionasymptotic expansionApplied mathematics. Quantitative methodsT57-57.97MathematicsQA1-939ENModern Stochastics: Theory and Applications, Vol 8, Iss 4, Pp 435-463 (2021) |
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Gaussian second-order moving average model conditional maximum likelihood estimators bias reduction asymptotic expansion Applied mathematics. Quantitative methods T57-57.97 Mathematics QA1-939 |
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Gaussian second-order moving average model conditional maximum likelihood estimators bias reduction asymptotic expansion Applied mathematics. Quantitative methods T57-57.97 Mathematics QA1-939 Fumiaki Honda Takeshi Kurosawa Bias reduction of a conditional maximum likelihood estimator for a Gaussian second-order moving average model |
| description |
In this study, we consider a bias reduction of the conditional maximum likelihood estimators for the unknown parameters of a Gaussian second-order moving average (MA(2)) model. In many cases, we use the maximum likelihood estimator because the estimator is consistent. However, when the sample size n is small, the error is large because it has a bias of $O({n^{-1}})$. Furthermore, the exact form of the maximum likelihood estimator for moving average models is slightly complicated even for Gaussian models. We sometimes rely on simpler maximum likelihood estimation methods. As one of the methods, we focus on the conditional maximum likelihood estimator and examine the bias of the conditional maximum likelihood estimator for a Gaussian MA(2) model. Moreover, we propose new estimators for the unknown parameters of the Gaussian MA(2) model based on the bias of the conditional maximum likelihood estimators. By performing simulations, we investigate properties of this bias, as well as the asymptotic variance of the conditional maximum likelihood estimators for the unknown parameters. Finally, we confirm the validity of the new estimators through this simulation study. |
| format |
article |
| author |
Fumiaki Honda Takeshi Kurosawa |
| author_facet |
Fumiaki Honda Takeshi Kurosawa |
| author_sort |
Fumiaki Honda |
| title |
Bias reduction of a conditional maximum likelihood estimator for a Gaussian second-order moving average model |
| title_short |
Bias reduction of a conditional maximum likelihood estimator for a Gaussian second-order moving average model |
| title_full |
Bias reduction of a conditional maximum likelihood estimator for a Gaussian second-order moving average model |
| title_fullStr |
Bias reduction of a conditional maximum likelihood estimator for a Gaussian second-order moving average model |
| title_full_unstemmed |
Bias reduction of a conditional maximum likelihood estimator for a Gaussian second-order moving average model |
| title_sort |
bias reduction of a conditional maximum likelihood estimator for a gaussian second-order moving average model |
| publisher |
VTeX |
| publishDate |
2021 |
| url |
https://doaj.org/article/cba596a44dff40e7a745555c81f32b27 |
| work_keys_str_mv |
AT fumiakihonda biasreductionofaconditionalmaximumlikelihoodestimatorforagaussiansecondordermovingaveragemodel AT takeshikurosawa biasreductionofaconditionalmaximumlikelihoodestimatorforagaussiansecondordermovingaveragemodel |
| _version_ |
1718425700154736640 |