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Identifiability and rates of estimation for scale parameters in location mixture models. (English) Zbl 0867.62010

Summary: 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 \(Y\), 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 [J. Heckman and B. Singer, Econometrica 52, 271-320 (1984; Zbl 0547.62077)] are not estimable at the usual parametric \(O_p(1/\sqrt{n})\) rate. The exact relationship between identifying constraints and achievable rates is explained.

MSC:

62F10 Point estimation
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62P20 Applications of statistics to economics

Citations:

Zbl 0547.62077
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References:

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