GENERALIZED OBSERVED BEST PREDICTION WITH EMPIRICAL BAYES PARAMETRIC BOOTSTRAP MODEL BUILDING

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2020

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Abstract

The observed best predictor (OBP) has been recently offered as a more robust alternative to the remarkable empirical best linear unbiased predictor (EBLUP). Although the latter has become a pervasive tool among applied statisticians, there are critical reasons why the OBP should almost always be used in conjunction with the EBLUP. In particular, mathematical models are often oversimplified or misspecified, lacking key predictors within the available set of data. For more complex models such as time-series applications, model robustness becomes even more imperative. We will provide some results related to the OBP theory and introduce a generalized, or weighted version of the OBP for different loss functions. This will first be defined on the Fay-Herriot model and then extended to the General Linear Mixed model. Finally, we will apply the best predictive estimator (BPE) to both parameter coefficients and variance parameters within the Fay-Herriot and cross-sectional time series models.

Model building strategies abound, and have continued to evolve. These are instrumental for applied statisticians and analysts passing judgement on whether statistical models are suitable for drawing conclusions or producing official estimates. A number of methodologies and approaches have been developed to consider this critical question of model selection and diagnostics. We endeavor to view this problem from the perspective of empirical Bayes (EB) - in a similar fashion as the EBLUP. As such, we define and develop an EB parametric bootstrap approach not only to estimate mean squared error, but also for finding the best model from a set of candidates (e.g., variable selection). This could be done for general criteria by considering leave-one-out predictive distributions. Once a viable model is selected, we can continue the model-building process by performing appropriate validation. Thus, the method is not only versatile, but has some computational advantages over other model building strategies.

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