Some diagnostic techniques for small area estimation : with applications to poverty mapping : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Statistics at Massey University, Palmerston North, New Zealand
Small area estimation (SAE) techniques borrow strength via auxiliary variables to provide reliable estimates at ﬁner geographical levels. An important application is poverty mapping,
whereby aid organisations distribute millions of dollars every year based on small area estimates of poverty measures. Therefore diagnostics become an important tool to ensure estimates
are reliable and funding is distributed to the most impoverished communities.
Small area models can be large and complex, however even the most complex models can
be of little use if they do not have predictive power at the small area level. This motivated a
variable importance measure for SAE that considers each auxiliary variable’s ability to explain
the variation in the dependent variable, as well as its ability to distinguish between the relative
levels in the small areas. A core question addressed is how candidate survey-based models
might be simpliﬁed without losing accuracy or introducing bias in the small area estimates.
When a small area estimate appears to be biased or unusual, it is important to investigate
and if necessary remedy the situation. A diagnostic is proposed that quantiﬁes the relative effect
of each variable, allowing identiﬁcation of any variables within an area that have a larger than
expected inﬂuence on the small area estimate for that area. This highlights possible errors which
need to be checked and if necessary corrected.
Additionally in SAE, it is essential that the estimates are at an acceptable level of precision
in order to be useful. A measure is proposed that takes the ratio of the variability in the small
areas to the uncertainty of the small area estimates. This measure is then used to assist in
determining the minimum level of precision needed in order to maintain meaningful estimates.
The diagnostics developed cover a wide range of small area estimation methods, consisting of those based on survey data only and those which combine survey and census data. By
way of illustration, the proposed methods are applied to SAE for poverty measures in Cambodia