Asymptotic properties of the maximum likelihood estimate in the first order autoregressive process |
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Authors: | Yasunori Fujikoshi Yoshimichi Ochi |
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Institution: | (1) Radiation Effect Research Foundation, Hiroshima University, Hiroshina, Japan |
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Abstract: | Summary In this paper we obtain an asymptotic expansion of the distribution of the maximum likelihood estimate (MLE)
based onT observations from the first order Gaussian process up to the term of orderT
−1. The expansion is used to compare
with a generalized estimate
including the least square estimate (LSE)
, based on the asymptotic probabilities around the true value of the estimates up to the terms of orderT
−1. It is shown that
(or the modified MLE
) is better than
(or the modified estimate
). Further, we note that
does not attain the bound for third order asymptotic median unbiased estimates. |
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Keywords: | Primary 62M10 Secondary 62E20 |
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