Advertisement

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)

Abstract

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.

Keywords

Asymptotic Distribution Maximum Order Autoregressive Process Regular Case Explosive Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations