Estimation and inference for area-wise spatial income distributions from grouped data. Estimating income distributions plays an important role in the measurement of inequality and poverty over space. The existing literature on income distributions predominantly focuses on estimating an income distribution for a country or a region separately and the simultaneous estimation of multiple income distributions has not been discussed in spite of its practical importance. To overcome the difficulty, effective methods are proposed for the simultaneous estimation and inference for area-wise spatial income distributions taking account of geographical information from grouped data. An efficient Bayesian approach to estimation and inference for area-wise latent parameters are developed, which gives area-wise summary measures of income distributions such as mean incomes and Gini indices, not only for sampled areas but also for areas without any samples thanks to the latent spatial state-space structure. The proposed method is demonstrated using the Japanese municipality-wise grouped income data. The simulation studies show the superiority of the proposed method to a crude conventional approach which estimates the income distributions separately. R code implementing the proposed methods is available at url{https://github.com/sshonosuke/SPID}.

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