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February 1999 Information in semiparametric mixtures of exponential families
Hemant Ishwaran
Ann. Statist. 27(1): 159-177 (February 1999). DOI: 10.1214/aos/1018031106


Z In a class of semiparametric mixture models, the score function (and consequently the effective information) for a finite-dimensional parameter can be made arbitrarily small depending upon the direction taken in the parameter space. This result holds for a broad range of semiparametric mixtures over exponential families and includes examples such as the gamma semiparametric mixture, the normal mean mixture, the Weibull semiparametric mixture and the negative binomial mixture. The near-zero information rules out the usual parametric $\sqrt{n}$ rate for the finite-dimensional parameter, but even more surprising is that the rate continues to be unattainable even when the mixing distribution is constrained to be countably discrete. Two key conditions which lead to a loss of information are the smoothness of the underlying density and whether a sufficient statistic is invertible.


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Hemant Ishwaran. "Information in semiparametric mixtures of exponential families." Ann. Statist. 27 (1) 159 - 177, February 1999.


Published: February 1999
First available in Project Euclid: 5 April 2002

zbMATH: 0932.62039
MathSciNet: MR1701106
Digital Object Identifier: 10.1214/aos/1018031106

Primary: 62G05
Secondary: 62B10, 62G20

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.27 • No. 1 • February 1999
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