### Abstract

Estimation for population subgroups or domains is investigated for model-assisted generalized regression (GREG) and model-dependent EBLUP estimators, under different model choices and under unequal probability sampling. Two particular issues are addressed: (i) how to account for the domain differences in the model formulation, and (ii) how to account for the underlying unequal probability sampling design. Results on bias and accuracy of GREG and EBLUP are based on Monte Carlo experiments where PPS samples were drawn from an artificially generated population. The bias of GREG estimator remained negligible for all model formulations considered, and accuracy improved when including the PPS size variable in the assisting model. A “double-use” of the auxiliary data both

in the sampling design and in the estimation design appeared favorable. In GREG, the mixed model formulation did not outperform the fixed-effects model formulation. For EBLUP, the model choice was critical and if not successful, large bias was introduced. For unweighted EBLUP, substantial bias reduction was attained with the inclusion of the PPS size variable in the model. We propose a new weighted EBLUP estimator for unequal probability sampling designs, as an alternative to the unweighted EBLUP. The results show that the weighted EBLUP behaves better that the unweighted EBLUP, but still the bias can be substantial and can dominate the MSE, which invalidates the construction of proper confidence intervals.

in the sampling design and in the estimation design appeared favorable. In GREG, the mixed model formulation did not outperform the fixed-effects model formulation. For EBLUP, the model choice was critical and if not successful, large bias was introduced. For unweighted EBLUP, substantial bias reduction was attained with the inclusion of the PPS size variable in the model. We propose a new weighted EBLUP estimator for unequal probability sampling designs, as an alternative to the unweighted EBLUP. The results show that the weighted EBLUP behaves better that the unweighted EBLUP, but still the bias can be substantial and can dominate the MSE, which invalidates the construction of proper confidence intervals.

Original language | English |
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Title of host publication | Proceedings of the Workshop on Survey Sampling Theory and Methodology, August 24-28, 2006, Ventspils, Latvia |

Number of pages | 10 |

Publication date | 2006 |

Pages | 35-44 |

Publication status | Published - 2006 |

MoE publication type | A4 Article in conference proceedings |

Event | Workshop on Survey Sampling Theory and Methodology - Riga, Poland Duration: 1 Jan 1800 → … |

### Fields of Science

- 112 Statistics and probability

### Cite this

Lehtonen, R. (2006). The role of models in model-assisted and model-dependent estimation for domains and small areas. In

*Proceedings of the Workshop on Survey Sampling Theory and Methodology, August 24-28, 2006, Ventspils, Latvia*(pp. 35-44)