Hierarchical Bayesian Small Area Models with Biased Auxiliary Variables
The small area estimation problem in sampling survey refers to the practical problem of sub-population estimation under a certain accuracy with a small sample size.Different from the design-based method,the model-based method does not rely on large sample theory and can use sample information from other small areas in the estimation process,which is more suitable for small area estimation problems.However,in reality,measurement errors cannot be completely avoided.When the model covariates are measured with error,the small area estimation results will be invalid.In this regard,the measurement error model is adopted to correct the errors of auxiliary variables,which performs small area estimation based on the unit-level hierarchical Bayes model,and estimates the error mechanism of auxiliary variables under the Bayesian framework.In view of the fact that in actual surveys,in order to facilitate data coding and statistics and control non-response errors,the survey results are mostly categorical data.Therefore,focusing on a model method is more suitable for small area estimation problems.For the situation where categorical auxiliary variables have measurement errors,the rationality of the method is proved.At the same time,its estimation effect is verified and practiced through simulation and empirical studies.Six common situations are simulated in practice and in addition to the situation where only categorical variables have measurement errors,it also considers the situation where the variables with measurement errors including both categorical and continuous variables.Numerical simulations and empirical results consistently show that the method in this paper can not only fully incorporate uncertainty factors related to inference and overcome the problem of limited sample size,but also has broad applicability.Compared with traditional methods,the estimation results are more robust while improving accuracy.
small area estimationhierarchical Bayesian modelmeasurement error modelcategorical variablesGibbs sampling
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