Supplement The Bound for the Asymptotic Distribution of Estimators when the Maximum Order of Consistency Depends on the Parameter

  • Masafumi Akahira
  • Kei Takeuchi
Part of the Lecture Notes in Statistics book series (LNS, volume 107)


In the regular case it is known that the order of consistency is equal to \(\sqrt{n}\), but in the non-regular case it is not always so, e.g. n1/α(0 < α < 2), \(\sqrt{n\;\textup{log}\ n}\) etc., which are independent of the unknown parameter (see Section 3.5 and also Akahira, 1975a; Akahira and Takeuchi, 1981; Vostrikova, 1984). In both cases the order of consistency is independent of θ. However, the order of consistency may depend on it in the case of the unstable and explosive process. Here a discussion on that will be done.


Asymptotic Distribution Maximum Order Autoregressive Process Regular Case Explosive Process 
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Copyright information

© Springer-Verlag New York, Inc. 1995

Authors and Affiliations

  • Masafumi Akahira
    • 1
  • Kei Takeuchi
    • 2
  1. 1.Institute of MathematicsUniversity of TsukubaIbarakiJapan
  2. 2.Meiji-Gakuin UniversityTotsukaku, YokohamaJapan

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