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On the asymptotic efficiency of estimators in an autoregressive process

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Let {X t } be defined recursively byX t =θX t−1+U t (t=1,2, ...), whereX 0=0 and {U t } is a sequence of independent identically distributed real random variables having a density functionf with mean 0 and varianceσ 2. We assume that |θ|<1. In the present paper we obtain the bound of the asymptotic distributions of asymptotically median unbiased (AMU) estimators of θ and the sufficient condition that an AMU estimator be asymptotically efficient in the sense that its distribution attains the above bound. It is also shown that the least squares estimator of θ is asymptotically efficient if and only iff is a normal density function.

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Authors
  1. Masafumi Akahira
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University of Electro-Communications

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Akahira, M. On the asymptotic efficiency of estimators in an autoregressive process. Ann Inst Stat Math 28, 35–48 (1976). https://doi.org/10.1007/BF02504729

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  • DOI: https://doi.org/10.1007/BF02504729

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