Advancing complex models in small area estimation and spatial statistics

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In survey sampling, policy decisions regarding allocation of resources to subgroups in a population, called small areas, are based on reliable predictors of their underlying parameters that describe resource use. However, the information is collected at a different scale than these subgroups. Hence we need to predict characteristics of the subgroups based on the coarser scale data. I plan to develop a frequentist approach for small area estimation of quantiles of Normal and non--Normal responses (e.g., median family income of small areas as Normal response). I am also interested in developing/extending my previous work in the linear mixed model (LMM) with the covariates subject to structural and functional measurement errors to non-Normal responses (e.g., binary or count response) using both frequentist and Bayesian approaches (will led by my first PhD student). My other project is to relax the linear regression assumption for the covariates of the LMM and replace them by a weaker assumption of a spline regression for the covariates subject to measurement errors (will led by my first MSc student). My plan is also to study non-ignorable missing responses and measurement errors in covariates for Normal and non-Normal responses (will led by my second PhD student).***In spatial statistics, I am pursuing research on the analysis of disease outcomes over space and time which falls under the umbrella of generalized additive mixed models. Spatio-temporal models are mainly used in disease mapping to provide a reliable estimate of the underlying disease risk by borrowing strength from neighbouring geographic sub-regions. One of my interests is to offer a frequentist approach based on maximum likelihood estimation (MLE) for complex spatio-temporal models of point-referenced datasets (also called geostatistics). In my previous work to account for seasonal effects in spatio--temporal models, I used generalized estimating equation (GEE) as an estimation approach assuming the independence structure for variance--covariance of outcome among regions which may lead to misspecification in some settings. My plan is to offer an alternative frequentist approach based on MLE to overcome this issue. My interest is also to develop mixtures of two (or more) spatial or spatio-temporal models, e.g. healthy and non-healthy populations, for disease mapping. Another project is to develop spatio-temporal for count data which may contain excess zeros because of immunity or other protective factors (will led by my second MSc student). I am also interested in working with spatial and spatio--temporal models with measurement errors (structural and functional) in covariates (will led by my third MSc student).***Ignoring proper modelling (based on the methods/models proposed above) may lead to wrong conclusions which can have clear policy implications in survey sampling and public health. *** *** *** **