Abstract
In this chapter, we construct the space of inference functions and information theoretic notions of E-sufficiency and E-ancillarity within this space. Let X be a sample space, and P be a class of probability measures P on X. For each PεP we let VP be the vector space of real valued functions f defined on the sample space X such that Ep[f(X)]2 < ∞. We introduce the usual inner product defined on VP,
Let θ be a real valued function on the class of probability measures P and define the parameter space θ = {θ(P); PεP}. Note that θ need not be a one to one functional. If it is, we call the model a one-parameter model.
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© 1988 Springer-Verlag New York Inc.
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McLeish, D.L., Small, C.G. (1988). The Space of Inference Functions: Ancillarity, Sufficiency and Projection. In: The Theory and Applications of Statistical Inference Functions. Lecture Notes in Statistics, vol 44. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3872-0_2
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DOI: https://doi.org/10.1007/978-1-4612-3872-0_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-96720-2
Online ISBN: 978-1-4612-3872-0
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