Comparison of Shift Experiments on a Banach Space

Harald Luschgy
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Harald Luschgy: University of Münster, Department of Mathematical Statistics

A chapter in Mathematical Statistics and Probability Theory, 1987, pp 217-230 from Springer

Abstract: Abstract The deficiency of one shift experiment relative to another on an infinite dimensional Banach space is studied. Under certain conditions, this deficiency is shown to be the supremum of the deficiencies between shift experiments defined by finite dimensional marginal distributions. Further, Boll’s “convolution divisibility” criterion for the ordering “being more informative” is extended to infinite dimensional spaces. More detailed results are given for shift experiments defined by Gaussian measures. In particular, the ordering “being more informative” can be characterized in terms of minimax risks.

Keywords: BANACH Space; Gaussian Measure; Reproduce Kernel Hilbert Space; Shift Experiment; Finite Dimensional Case (search for similar items in EconPapers)
Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-3963-9_16

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DOI: 10.1007/978-94-009-3963-9_16

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