Non-Regular Statistical Estimation

  • Masafumi Akahira
  • Kei Takeuchi

Part of the Lecture Notes in Statistics book series (LNS, volume 107)

About this book


In order to obtain many of the classical results in the theory of statistical estimation, it is usual to impose regularity conditions on the distributions under consideration. In small sample and large sample theories of estimation there are well established sets of regularity conditions, and it is worth while to examine what may follow if any one of these regularity conditions fail to hold. "Non-regular estimation" literally means the theory of statistical estimation when some or other of the regularity conditions fail to hold. In this monograph, the authors present a systematic study of the meaning and implications of regularity conditions, and show how the relaxation of such conditions can often lead to surprising conclusions. Their emphasis is on considering small sample results and to show how pathological examples may be considered in this broader framework.


Estimator Lemma Likelihood Variance distribution form framework information minimum probability proof set sets statistics theorem

Authors and affiliations

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

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York 1995
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-94578-1
  • Online ISBN 978-1-4612-2554-6
  • Series Print ISSN 0930-0325
  • Buy this book on publisher's site