Invariance Properties

  • Lucien Le Cam
Part of the Springer Series in Statistics book series (SSS)


In this chapter we describe briefly certain properties that arise when a group of transformations acts on the index set Θ of an experiment ℰ = {Pθ; θ∈Θ}. This situation occurs in several different contexts. One of them leads to a form of Hájek’s convolution theorem. Another reason for the study of invariance properties comes from the very common practice of taking limiting distributions of estimates, say X n , by rescaling and investigating expressions such as δ n −1 (X n − θ) with a sequence {δn}, δ n > 0, which tends to zero. The chapter is divided into sections as follows.


Compact Group Haar Measure Invariance Property Radon Measure Exponential Family 
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Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • Lucien Le Cam
    • 1
  1. 1.Department of StatisticsUniversity of CaliforniaBerkeleyUSA

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