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**Small area estimation of general parameters with application to poverty indicators: a hierarchical Bayes approach.**
*(English)*
Zbl 1454.62489

Summary: Poverty maps are used to aid important political decisions such as allocation of development funds by governments and international organizations. Those decisions should be based on the most accurate poverty figures. However, often reliable poverty figures are not available at fine geographical levels or for particular risk population subgroups due to the sample size limitation of current national surveys. These surveys cannot cover adequately all the desired areas or population subgroups and, therefore, models relating the different areas are needed to “borrow strength” from area to area. In particular, the Spanish Survey on Income and Living Conditions (SILC) produces national poverty estimates but cannot provide poverty estimates by Spanish provinces due to the poor precision of direct estimates, which use only the province specific data. It also raises the ethical question of whether poverty is more severe for women than for men in a given province. We develop a hierarchical Bayes (HB) approach for poverty mapping in Spanish provinces by gender that overcomes the small province sample size problem of the SILC. The proposed approach has a wide scope of application because it can be used to estimate general nonlinear parameters. We use a Bayesian version of the nested error regression model in which Markov chain Monte Carlo procedures and the convergence monitoring therein are avoided. A simulation study reveals good frequentist properties of the HB approach. The resulting poverty maps indicate that poverty, both in frequency and intensity, is localized mostly in the southern and western provinces and it is more acute for women than for men in most of the provinces.

### MSC:

62P20 | Applications of statistics to economics |

62D05 | Sampling theory, sample surveys |

62F15 | Bayesian inference |

91B82 | Statistical methods; economic indices and measures |

### Keywords:

hierarchical Bayes; mixed linear model; nested error linear regression model; noninformative priors; poverty mapping; small area estimation### Software:

WinBUGS
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\textit{I. Molina} et al., Ann. Appl. Stat. 8, No. 2, 852--885 (2014; Zbl 1454.62489)

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