B1703
Title: Nonparametric empirical Bayes prediction in mixed models
Authors: Trambak Banerjee - University of Kansas (United States) [presenting]
Padma Sharma - Federal Reserve Bank of Kansas City (United States)
Abstract: Mixed models are classical tools for modelling repeated data on subjects, such as data on patients collected over time. These models extend conventional linear models to include random effects, that capture between-subject variation and accommodate dependence within the repeated measurements of a subject. Traditionally, predictions in mixed models are conducted by assuming that the random effects have a zero mean Normal distribution, which leads to the classical best linear unbiased predictor (BLUP) of the random effects in these models. However, such a distributional assumption on the random effects is restrictive and may lead to inefficient predictions, especially when the true random effect distribution is far from Normal. An empirical Bayes prediction framework, EBPred, is developed for mixed models. The predictions from EBPred rely on the best predictor of the random effects, which are constructed without any parametric assumption on the distribution of the random effects and offer a natural extension to the BLUP when the true random effect distribution is not Normal. It is shown that the predictions from EBPred are asymptotically optimal in terms of mean squared error for prediction. The simulation study and a real data analysis demonstrate that EBPred outperforms existing predictive rules in mixed models.
