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首页> 外文期刊>journal of time series analysis >OPTIMALITY OF THE MAXIMUM LIKELIHOOD ESTIMATOR IN FIRST‐ORDER AUTOREGRESSIVE PROCESSES
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OPTIMALITY OF THE MAXIMUM LIKELIHOOD ESTIMATOR IN FIRST‐ORDER AUTOREGRESSIVE PROCESSES

机译：OPTIMALITY OF THE MAXIMUM LIKELIHOOD ESTIMATOR IN FIRST‐ORDER AUTOREGRESSIVE PROCESSES

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Abstract.Let ρρ* be the maximum likelihood estimator (MLE) of the parameter ρ in the first‐order autoregressive process with normal errors. The problem of optimality in the sense of weighted squared error is considered rather than moments of asymptotic distributions. Many unbiased estimators can be constructed, but the two‐dimensional sufficient statistic is incomplete. It is shown that dEρ* ‐ ρ→ 0 uniformly in ρ, and thatdE(ρ*)/dρ→ 1 for all ρ>1. For ρ>1, it is known that the asymptotic distribution of {I(ρ)}12(ρ* ‐ ρ), whereI(ρ) is the Fisher information, is Cauchy. It follows that the Cramèr‐Rao inequality will not yield useful results for investigating the limit of exact efficiency of any asymptotically unbiased estimator, including the MLE. For all ρ<1, ρ* is asymptotically optimal in the sense of minimizing expected weighted squared error. In addition, for ρ<1, ρ* minim

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