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 −1 n (X n − θ) with a sequence {δn}, δ n > 0, which tends to zero. The chapter is divided into sections as follows.
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© 1986 Springer-Verlag New York Inc.
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Cam, L.L. (1986). Invariance Properties. In: Asymptotic Methods in Statistical Decision Theory. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4946-7_8
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DOI: https://doi.org/10.1007/978-1-4612-4946-7_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-9369-9
Online ISBN: 978-1-4612-4946-7
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