That Prasad-Rao is Robust: Estimation of MSPE of OBP under Potential Model Misspecification
We consider estimation of the mean squared prediction error (MSPE) of the observed best predictor (OBP) in small area estimation under an area-level model with potential model misspecification. It was previously thought that the traditional Prasad-Rao (P-R) linearization method could not be used, because it is derived under the assumption that the underlying model is correctly specified. However, we show that, when it comes to estimating the unconditional MSPE, the PR estimator, derived for estimating the MSPE of OBP assuming that the underlying model is correct, remains first-order unbiased even when the underlying model is misspecified in its mean function. A second-order unbiased estimator of the MSPE is derived by modifying the PR MSPE estimator. The PR and modified PR estimators also have much smaller variation compared to the existing MSPE estimators for OBP. The theoretical findings are supported by empirical results including simulation studies and real-data applications. This work is joint with Xiaohui Liu and Haiqiang Ma of Jiangxi University of Finance and Economics.
]]>We consider estimation of the mean squared prediction error (MSPE) of the observed best predictor (OBP) in small area estimation under an area-level model with potential model misspecification. It was previously thought that the traditional Prasad-Rao (P-R) linearization method could not be used, because it is derived under the assumption that the underlying model is correctly specified. However, we show that, when it comes to estimating the unconditional MSPE, the PR estimator, derived for estimating the MSPE of OBP assuming that the underlying model is correct, remains first-order unbiased even when the underlying model is misspecified in its mean function. A second-order unbiased estimator of the MSPE is derived by modifying the PR MSPE estimator. The PR and modified PR estimators also have much smaller variation compared to the existing MSPE estimators for OBP. The theoretical findings are supported by empirical results including simulation studies and real-data applications. This work is joint with Xiaohui Liu and Haiqiang Ma of Jiangxi University of Finance and Economics.
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