The Annals of Statistics

Identifiability and rates of estimation for scale parameters in location mixture models

Hemant Ishwaran

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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.

Article information

Ann. Statist., Volume 24, Number 4 (1996), 1560-1571.

First available in Project Euclid: 17 September 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation
Secondary: 62G20: Asymptotic properties 62P20: Applications to economics [See also 91Bxx]

Weibull semiparametric mixture mixture model structural parameter


Ishwaran, Hemant. Identifiability and rates of estimation for scale parameters in location mixture models. Ann. Statist. 24 (1996), no. 4, 1560--1571. doi:10.1214/aos/1032298284.

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