Bias reduction of the maximum-likelihood estimator for a conditional Gaussian MA(1) model |
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Authors: | Takeshi Kurosawa Kohei Noguchi Fumiaki Honda |
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Affiliation: | 1. Department of Applied Mathematics, Faculty of Science, Tokyo University of Science, Tokyo, Japan;2. Department of Mathematical Information Science, Graduate School of Science, Tokyo University of Science, Tokyo, Japan |
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Abstract: | In this paper, we consider an estimation for the unknown parameters of a conditional Gaussian MA(1) model. In the majority of cases, a maximum-likelihood estimator is chosen because the estimator is consistent. However, for small sample sizes the error is large, because the estimator has a bias of O(n? 1). Therefore, we provide a bias of O(n? 1) for the maximum-likelihood estimator for the conditional Gaussian MA(1) model. Moreover, we propose new estimators for the unknown parameters of the conditional Gaussian MA(1) model based on the bias of O(n? 1). We investigate the properties of the bias, as well as the asymptotical variance of the maximum-likelihood estimators for the unknown parameters, by performing some simulations. Finally, we demonstrate the validity of the new estimators through this simulation study. |
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Keywords: | Asymptotic expansion bias reduction Gaussian MA(1) model maximum-likelihood estimator. |
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