Seminar

Semi-parametric Small Area Estimation for Discrete Outcomes

Nikolaos Tzavidis (University of Southampton)

May 14, 2013, 14:00–15:30

Toulouse

Room MF 323

Statistics Seminar

Abstract

The increasing demand for reliable small area statistics has led to the development of a number of efficient model-based small area estimation (SAE) methods (Rao, 2003). For example, the empirical best linear unbiased predictor (EBLUP) based on a linear mixed model (LMM) is often recommended when the target of inference is the small area average of a continuous response variable (Battese et al., 1988). Using a mixed model, however, requires strong distributional assumptions. Robust SAE inference under the LMM has recently attracted some interest (Sinha & Rao, 2009; Chambers et al., 2013). An alternative approach to small area estimation that automatically allows for robust inference is to use M-quantile models (Chambers & Tzavidis, 2006; Chambers et al., 2013). Many survey variables are categorical in nature and are therefore not suited to standard SAE methods based on LMMs. In this presentation we discuss recent work on a new approach to SAE for discrete outcomes based on M-quantile modelling. This is based on extending the existing M-quantile approach for continuous outcomes to the case where the response is discrete (binary or a count). As with M-quantile modelling of a continuous response (Chambers & Tzavidis, 2006) random effects are avoided and between area variation in the response is characterised by variation in area-specific values of quantile-like coefficients. After reviewing M-quantile small area estimation for a continuous response, we show how the approach for robust inference for generalised linear models (GLMs) proposed by Cantoni & Ronchetti (2001) can be extended for fitting an M-quantile GLM. Approaches for defining the M-quantile coefficients, which play the role of pseudo-random effects in this framework, are discussed, alongside the definition of small area predictors and corresponding MSE estimators. Results from model-based studies aimed at empirically assessing the performance of the proposed small area predictors are presented.