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.
- Mixture model
- Structural parameter
- Weibull semiparametric mixture
ASJC Scopus subject areas
- Statistics and Probability