A note on insufficiency and the preservation of Fisher information

Details A note on insufficiency and the preservation of Fisher information A note on insufficiency and the preservation of Fisher information

2011-07-19

arxiv.org/abs/1107.3797v2

Mathematics

Statistics Theory

Contribution to a volume in honor of Jon Wellner's 65th birthday (revised)

Scientific paper

Kagan and Shepp (2005, Amer. Statist.) presented an elegant example of a
mixture model for which an insufficient statistic preserves Fisher information.
This note uses the regularity property of differentiability in quadratic mean
to provide another explanation for the phenomenon they observed. Some
connections with Le Cam's theory for convergence of experiments are noted.

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