### 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 O_{p}(1/ √n) rate. The exact relationship between identifying constraints and achievable rates is explained.

Original language | English |
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Pages (from-to) | 1560-1571 |

Number of pages | 12 |

Journal | Annals of Statistics |

Volume | 24 |

Issue number | 4 |

State | Published - Aug 1 1996 |

Externally published | Yes |

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### Keywords

- Mixture model
- Structural parameter
- Weibull semiparametric mixture

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

*Annals of Statistics*,

*24*(4), 1560-1571.