Abstract

Small area inference based on mixed models, i.e. models that contain both fixed and
random effects, are the industry standard for this field, allowing between area
heterogeneity to be represented by random area effects. Use of the linear mixed model
is ubiquitous in this context, with maximum likelihood, or its close relative, REML,
the standard method for estimating the parameters of this model. These parameter
estimates, and in particular the resulting predicted values of the random area effects,
are then used to construct empirical best linear unbiased predictors (EBLUPs) of the
unknown small area means. It is now well known that the EBLUP can be unstable
when there are outliers in sample data, and an outlierrobust EBLUP, or REBLUP, has
been proposed by Sinha and Rao (2009), based on modifying the parameter estimating
functions to make them less sensitive to sample outliers. Unfortunately, these
modified estimating functions can be numerically unstable, and mean squared error
estimation for the REBLUP is not straightforward. Taking a somewhat different
approach, Chambers and Mokhtarian (2013) proposed an outlier robust block
bootstrap approach to fitting a linear mixed model in the presence of both area level
and unit level outliers. A natural extension of this bounded block bootstrap can then be
used to define an outlier robust version of the EBLUP and a simple way of estimating
its mean squared error. This approach is described in this paper, together with
simulation results that provides some evidence for our claim that the new method is
robust to the influence of outliers. In particular, it leads to an easily computed version
of the REBLUP and an easily computed and stable estimate of its mean squared error.