A Semiparametric Estimator of Random Eeects

The use of a linear estimator to estimate random eeects in a Mixed Model is not necessarily optimal if the prior distribution is non-normal. Either a frequentist or Bayesian approach leads to the Best Linear Unbiased Predictor (BLUP), but an empirical Bayes approach produces a multivariate, non-linear, single-pass kernel-based estimator (the General Empirical Bayes or GEB es-timator) that allows relaxed distributional assumptions on the parameters. A suitable loss function is motivated to allow selection of a bandwidth. This loss function requires a technical modii-cation to the familiar kernel form, and this modiied estimator is shown to be asymptotically optimal. 2 3 The GEB estimator is implemented using Splus software. We introduce a class of densities which allow a rotation to independence , and restrict attention to these densities. Simulated longitudinal studies allow comparison of the GEB estimator with the BLUP using three diierent classes of priors. The GEB is found to outperform the BLUP when the prior is Cauchy and for some normal mixtures.