### Abstract

Hybrid calibration refers to an approach where techniques of classical calibration and more recent model-assisted calibration are combined for a joint calibration methodology. The classical calibration does not assume a model but uses the original auxiliary data as aggregates, whereas in model calibration, unit-level predictions from a model are used as "pseudo" auxiliary information. By combining these approaches we introduce "hybrid" methods, where aggregate data from different levels of the population are supplied to the model-free component and unit-level data are incorporated into the model-assisted component, where the model is chosen according to the type of the target variable. We used linear and logistic models in our studies. In the estimation for population subgroups or domains, the classical calibration fails when domain sample sizes become small, restricting the use of the method in small domain estimation. Our hybrid calibration methods attained acceptable precision for small domains, thus extending the applicability of the calibration approach for small domain estimation. In our studies, the basic model-assisted calibration was usually the best in accuracy, but the method requires population-level information on auxiliary variables in the model. The basic hybrid calibration method overcomes this restriction by including a model-free calibration component in the model-assisted calibration procedure. A new two-level hybrid calibration technique provides a further extension applicable for hierarchically structured populations. In this method, calibration in the model-free part is performed at a higher regional level, instead of the domain level as in the other methods, providing much flexibility in the use of auxiliary data. Although the method is defined as an indirect estimation method, it appeared nearly design unbiased, similarly as the other calibration methods discussed. The method provided good accuracy for small domains in the experiments conducted in our studies, and the weight distributions were as stable as for the basic model-assisted calibration. Most stable distributions of weights were observed with weights attached to the Hájek type estimators developed in the paper.

Key Words

Auxiliary information, model-assisted calibration, mixed models, survey weights, design-based simulation experiments

Original language | English |
---|---|

Journal | Statistica & Applicazioni |

ISSN | 1824-6672 |

Publication status | Submitted - 2019 |

MoE publication type | A1 Journal article-refereed |

### Fields of Science

- 112 Statistics and probability

### Cite this

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**Hybrid calibration methods for small domain estimation.** / Lehtonen, Risto; Veijanen, Ari.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Hybrid calibration methods for small domain estimation

AU - Lehtonen, Risto

AU - Veijanen, Ari

PY - 2019

Y1 - 2019

N2 - AbstractHybrid calibration refers to an approach where techniques of classical calibration and more recent model-assisted calibration are combined for a joint calibration methodology. The classical calibration does not assume a model but uses the original auxiliary data as aggregates, whereas in model calibration, unit-level predictions from a model are used as "pseudo" auxiliary information. By combining these approaches we introduce "hybrid" methods, where aggregate data from different levels of the population are supplied to the model-free component and unit-level data are incorporated into the model-assisted component, where the model is chosen according to the type of the target variable. We used linear and logistic models in our studies. In the estimation for population subgroups or domains, the classical calibration fails when domain sample sizes become small, restricting the use of the method in small domain estimation. Our hybrid calibration methods attained acceptable precision for small domains, thus extending the applicability of the calibration approach for small domain estimation. In our studies, the basic model-assisted calibration was usually the best in accuracy, but the method requires population-level information on auxiliary variables in the model. The basic hybrid calibration method overcomes this restriction by including a model-free calibration component in the model-assisted calibration procedure. A new two-level hybrid calibration technique provides a further extension applicable for hierarchically structured populations. In this method, calibration in the model-free part is performed at a higher regional level, instead of the domain level as in the other methods, providing much flexibility in the use of auxiliary data. Although the method is defined as an indirect estimation method, it appeared nearly design unbiased, similarly as the other calibration methods discussed. The method provided good accuracy for small domains in the experiments conducted in our studies, and the weight distributions were as stable as for the basic model-assisted calibration. Most stable distributions of weights were observed with weights attached to the Hájek type estimators developed in the paper.Key WordsAuxiliary information, model-assisted calibration, mixed models, survey weights, design-based simulation experiments

AB - AbstractHybrid calibration refers to an approach where techniques of classical calibration and more recent model-assisted calibration are combined for a joint calibration methodology. The classical calibration does not assume a model but uses the original auxiliary data as aggregates, whereas in model calibration, unit-level predictions from a model are used as "pseudo" auxiliary information. By combining these approaches we introduce "hybrid" methods, where aggregate data from different levels of the population are supplied to the model-free component and unit-level data are incorporated into the model-assisted component, where the model is chosen according to the type of the target variable. We used linear and logistic models in our studies. In the estimation for population subgroups or domains, the classical calibration fails when domain sample sizes become small, restricting the use of the method in small domain estimation. Our hybrid calibration methods attained acceptable precision for small domains, thus extending the applicability of the calibration approach for small domain estimation. In our studies, the basic model-assisted calibration was usually the best in accuracy, but the method requires population-level information on auxiliary variables in the model. The basic hybrid calibration method overcomes this restriction by including a model-free calibration component in the model-assisted calibration procedure. A new two-level hybrid calibration technique provides a further extension applicable for hierarchically structured populations. In this method, calibration in the model-free part is performed at a higher regional level, instead of the domain level as in the other methods, providing much flexibility in the use of auxiliary data. Although the method is defined as an indirect estimation method, it appeared nearly design unbiased, similarly as the other calibration methods discussed. The method provided good accuracy for small domains in the experiments conducted in our studies, and the weight distributions were as stable as for the basic model-assisted calibration. Most stable distributions of weights were observed with weights attached to the Hájek type estimators developed in the paper.Key WordsAuxiliary information, model-assisted calibration, mixed models, survey weights, design-based simulation experiments

KW - 112 Statistics and probability

M3 - Article

JO - Statistica & Applicazioni

JF - Statistica & Applicazioni

SN - 1824-6672

ER -