Asymptotic properties of the maximum likelihood estimate in the first order autoregressive process期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Asymptotic properties of the maximum likelihood estimate in the first order autoregressive process

Authors:	Yasunori Fujikoshi Yoshimichi Ochi

Institution:	(1) Radiation Effect Research Foundation, Hiroshima University, Hiroshina, Japan

Abstract:	Summary In this paper we obtain an asymptotic expansion of the distribution of the maximum likelihood estimate (MLE) $\hat \alpha _{ML}$ based onT observations from the first order Gaussian process up to the term of orderT ⁻¹. The expansion is used to compare $\hat \alpha _{ML}$ with a generalized estimate $\hat \alpha _{c_1 ,c_2 }$ including the least square estimate (LSE) $\hat \alpha _{LS}$ , based on the asymptotic probabilities around the true value of the estimates up to the terms of orderT ⁻¹. It is shown that $\hat \alpha _{ML}$ (or the modified MLE $\hat \alpha _{ML}^$ ) is better than $\hat \alpha _{c_1 ,c_2 }$ (or the modified estimate $\hat \alpha _{c_1 ,c_2 }^$ ). Further, we note that $\hat \alpha _{ML}^*$ does not attain the bound for third order asymptotic median unbiased estimates.

Keywords:	Primary 62M10 Secondary 62E20
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