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IPS192 Hukum C. et al.

Small area prediction of counts under
nonparametric generalized linear mixed model
2
3
Hukum Chandra , Nicola Salvati , Ray Chambers
1
1 Indian Agricultural Statistics Research Institute, Library Avenue, India
2 University of Pisa, Italy
3 University of Wollongong, Wollongong, Australia

Abstract
We describe a methodology for small area estimation of counts that assumes
an area-level version of a nonparametric generalized linear mixed model with
a mean structure defined using spatial splines. The proposed method
represents an alternative to other small area estimation methods based on
area level spatial models that are designed for both spatially stationary and
spatially non-stationary populations. We develop an estimator for the mean
squared error of the proposed small area predictor as well as an approach for
testing for the presence of spatial structure in the data and evaluate both the
proposed small area predictor and its mean squared error estimator via
simulations studies. Our empirical results show that when data are spatially
non-stationary the proposed small area predictor outperforms other area level
estimators in common use and that the proposed MSE estimator tracks the
actual mean squared error reasonably well, with confidence intervals based on
it achieving close to nominal coverage. An application to poverty estimation
using household consumer expenditure survey data from 2011-12 collected
by the national sample survey office of India is considered.

Keywords
Small area estimation; Nonparametric models; Spatial relationship; Count
data; Poverty indicator

1. Introduction
When the variable of interest is binary or a count and small area estimates
are required for these data, use of standard small area estimation (SAE)
methods based on linear mixed models becomes problematic. For example,
poverty indicators and many other indicators related to socio-economic status
and food insecurity usually behave in a non-Gaussian manner at small area
levels, and so estimation in these cases is typically based on a generalized
linear mixed model (GLMM); see Manteiga et al. (2007) and Ruppert et al.
(2003, chapter 10). In many applications this is not possible, for example
poverty mapping where data confidentiality restricts access to unit level survey
data with small area identifiers, or where the agency carrying out the small
area analysis does not have the resources to analyse unit level data, as in many

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