## The Annals of Statistics

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

Hemant Ishwaran

#### Abstract

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

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

Dates
First available in Project Euclid: 17 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1032298284

Digital Object Identifier
doi:10.1214/aos/1032298284

Mathematical Reviews number (MathSciNet)
MR1416649

Zentralblatt MATH identifier
0867.62010

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

#### Citation

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. https://projecteuclid.org/euclid.aos/1032298284

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• OTTAWA, ONTARIO CANADA K1N 6N5 E-MAIL: ishwaran@expresso. mathstat.uottawa.ca