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Invariance Properties

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

Abstract

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.

Keywords

Compact Group Haar Measure Invariance Property Radon Measure Exponential Family 
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.

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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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