Premium
Hierarchical Bayes small‐area estimation with an unknown link function
Author(s) -
Sugasawa Shonosuke,
Kubokawa Tatsuya,
Rao J. N. K.
Publication year - 2019
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12376
Subject(s) - bayes' theorem , markov chain monte carlo , mathematics , small area estimation , markov chain , function (biology) , link (geometry) , spline (mechanical) , estimation , statistics , econometrics , monte carlo method , computer science , algorithm , bayesian probability , evolutionary biology , biology , management , structural engineering , combinatorics , estimator , economics , engineering
Area‐level unmatched sampling and linking models have been widely used as a model‐based method for producing reliable estimates of small‐area means. However, one practical difficulty is the specification of a link function. In this paper, we relax the assumption of a known link function by not specifying its form and estimating it from the data. A penalized‐spline method is adopted for estimating the link function, and a hierarchical Bayes method of estimating area means is developed using a Markov chain Monte Carlo method for posterior computations. Results of simulation studies comparing the proposed method with a conventional approach based on a known link function are presented. In addition, the proposed method is applied to data from the Survey of Family Income and Expenditure in Japan and poverty rates in Spanish provinces.