Advancing complex models in small area estimation and spatial statistics

在调查抽样中，关于将资源分配给人口中称为小区域的子组的政策决定，是基于对描述资源使用的基本参数的可靠预测。然而，收集信息的规模与这些小组不同。因此，我们需要基于较粗的尺度数据来预测子群的特征。我计划开发一种频率法来估计小区域正常和非正常反应的分位数(例如，小地区的家庭收入中位数作为正常反应)。我还有兴趣发展/扩展我以前在线性混合模型(LMM)中的工作，使用频率和贝叶斯方法(将由我的第一个博士生领导)将受结构和功能测量误差影响的协变量扩展到非正态响应(例如，二进制或计数响应)。我的另一个项目是放松对LMM协变量的线性回归假设，并用一个较弱的假设取而代之，即对受测量误差影响的协变量进行样条式回归(将由我的第一个硕士学生领导)。我的计划也是研究正常和非正常反应的协变量中不可忽视的缺失反应和测量误差(将由我的第二个博士生领导)。*在空间统计学方面，我正在进行广义可加混合模型下的疾病结果的空间和时间分析研究。时空模型主要用于疾病测绘，通过借用邻近地理分区域的力量来提供对潜在疾病风险的可靠估计。我的兴趣之一是提供一种基于最大似然估计(MLE)的频域方法，用于点参考数据集的复杂时空模型(也称为地统计学)。在我以前解释时空模型中季节性效应的工作中，我使用广义估计方程(GEE)作为一种估计方法，假设方差--地区之间结果的协方差--的独立结构，在某些情况下可能导致错误的指定。我的计划是提供一种基于MLE的替代频率法来克服这个问题。我的兴趣也是开发两个(或更多)空间或时空模型的混合，例如健康和非健康人口，用于绘制疾病地图。另一个项目是开发时空计数数据，这些数据可能因为免疫或其他保护因素而包含过多的零(将由我的第二个理学硕士学生领导)。我还对协变量中有测量误差(结构和功能)的空间和时空模型感兴趣(将由我的第三个硕士学生领导)。*忽略适当的建模(基于上面建议的方法/模型)可能会导致错误的结论，这可能会在调查抽样和公共卫生中产生明确的政策含义。*

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. *** *** *** **