Open Access
August 1996 Identifiability and rates of estimation for scale parameters in location mixture models
Hemant Ishwaran
Ann. Statist. 24(4): 1560-1571 (August 1996). DOI: 10.1214/aos/1032298284


In this paper we consider the problem of identifiability and estimation for the scale parameter $\theta$ in the location mixture model $\theta (X + Y)$, where X has a known distribution independent of the Y, whose distribution is unknown. Identification of $\theta$ is ensured by constraining Y based on the tail behavior of the distribution for X. Rates for estimation are described for those X which can be written as a square summable series of exponential variables. As a special case, our analysis shows that the structural parameters in the Weibull semiparametric mixture (Heckman and Singer) are not estimable at the usual parametric $O_p(1/ \sqrt{n})$. The exact relationship between identifying constraints and achievable rates is explained.


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Hemant Ishwaran. "Identifiability and rates of estimation for scale parameters in location mixture models." Ann. Statist. 24 (4) 1560 - 1571, August 1996.


Published: August 1996
First available in Project Euclid: 17 September 2002

zbMATH: 0867.62010
MathSciNet: MR1416649
Digital Object Identifier: 10.1214/aos/1032298284

Primary: 62G05
Secondary: 62G20 , 62P20

Keywords: mixture model , structural parameter , Weibull semiparametric mixture

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 4 • August 1996
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