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

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Abstract

In this paper we consider the problem of identifiability and estimation for the scale parameter θ in the location mixture model θ(X + Y), where X has a known distribution independent of the Y, whose distribution is unknown. Identification of θ 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 Op(1/ √n) rate. The exact relationship between identifying constraints and achievable rates is explained.

Original languageEnglish
Pages (from-to)1560-1571
Number of pages12
JournalAnnals of Statistics
Volume24
Issue number4
StatePublished - Aug 1 1996
Externally publishedYes

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Keywords

  • Mixture model
  • Structural parameter
  • Weibull semiparametric mixture

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

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