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Adaptive estimates for autoregressive processes

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Abstract

Let {X t :t=0, ±1, ±2, ...} be a stationaryrth order autoregressive process whose generating disturbances are independent identically distributed random variables with marginal distribution functionF. Adaptive estimates for the parameters of {X t } are constructed from the observed portion of a sample path. The asymptotic efficiency of these estimates relative to the least squares estimates is greater than or equal to one for all regularF. The nature of the adaptive estimates encourages stable behavior for moderate sample sizes. A similar approach can be taken to estimation problems in the general linear model.

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Authors and Affiliations

  1. University of California, Berkeley

    Rudolf Beran

Authors
  1. Rudolf Beran
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Additional information

This research was partially supported by National Science Foundation Grant GP-31091X. American Mathematical Society 1970 subject classification. Primary 62N10; Secondary 62G35. Key words and phrases: autoregressive process, adaptive estimates, robust estimates.

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Beran, R. Adaptive estimates for autoregressive processes. Ann Inst Stat Math 28, 77–89 (1976). https://doi.org/10.1007/BF02504731

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  • DOI: https://doi.org/10.1007/BF02504731

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