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We introduce a new small area predictor when the Fay-Herriot normal errormodel is fitted to a logarithmically transformed response variable, and thecovariate is measured with error. This framework has been previously studied byMosaferi et al. (2023). The empirical predictor given in their manuscriptcannot perform uniformly better than the direct estimator. Our proposedpredictor in this manuscript is unbiased and can perform uniformly better thanthe one proposed in Mosaferi et al. (2023). We derive an approximation of themean squared error (MSE) for the predictor. The prediction intervals based onthe MSE suffer from coverage problems. Thus, we propose a non-parametricbootstrap prediction interval which is more accurate. This problem is of greatinterest in small area applications since statistical agencies and agriculturalsurveys are often asked to produce estimates of right skewed variables withcovariates measured with errors. With Monte Carlo simulation studies and twoCensus Bureau's data sets, we demonstrate the superiority of our proposedmethodology.

An Unbiased Predictor for Skewed Response Variable with Measurement Error in Covariate