Open Access
VOL. 9 | 2013 A note on insufficiency and the preservation of Fisher information
David Pollard

Editor(s) M. Banerjee, F. Bunea, J. Huang, V. Koltchinskii, M. H. Maathuis

Inst. Math. Stat. (IMS) Collect., 2013: 266-275 (2013) DOI: 10.1214/12-IMSCOLL919


Kagan and Shepp [ The American Statistician 59 (2005) 54–56] 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.


Published: 1 January 2013
First available in Project Euclid: 8 March 2013

zbMATH: 1346.62006
MathSciNet: MR3202639

Digital Object Identifier: 10.1214/12-IMSCOLL919

Primary: 60K35 , 60K35
Secondary: 60K35

Keywords: differentiability in quadratic mean , Fisher information , Hellinger differentiability of probability models , Le Cam’s distance between statistical models , score function , sufficiency

Rights: Copyright © 2010, Institute of Mathematical Statistics

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