Advancing Statistical Models for Complex and Correlated Data

在小区域估计（SAE）中，关于将资源分配给人口的子群体的政策决策依赖于其潜在参数的可靠预测因子。然而，在一些亚群体中，由于相对于总体而言样本量小而被称为小区域，通常无法获得可靠预测所需的信息。因此，调查（或行政）数据在较粗的尺度被用来预测小区域的特征。混合模式主要用于从其他来源（例如，以前的调查、行政和人口普查数据集）借用信息，以提供可靠的预测。这种预测有许多应用，例如，在疾病制图中，主要目标是在小区域内找到可靠的疾病发病率，例如癌症。它在农业、经济、政策制定和资金分配方面也有其他应用。在未来的5年里，我将继续在SAE的背景下开发新的和原创的模型。我的计划是做10个项目来处理不可忽略的缺失协变量；分位数反应;健壮的统计;纵向数据中协变量的测量误差一类广义线性混合模型的非参数响应。在空间统计学方面，我的研究方向是疾病发病率在空间和时间上的分析。一般来说，这些时空模型属于混合模型的范畴。时空模型主要用于疾病制图，通过借鉴邻近地理子区域的优势，提供对潜在疾病风险的可靠估计。疾病发病率空间和时空模型发展背后的理念对于模拟真实发病率的变化和更好地将系统变动性与随机噪声区分开来至关重要，随机噪声通常掩盖了粗糙的发病率地图。在未来的5年里，我将继续在我的研究项目中开发新的和原创的时空模型。我的计划是从事9个项目，处理点参考数据集的复杂时空模型的最大似然估计（MLE）；空间或时空模型混合的健壮版本；MLE用于两种或多种相关疾病的联合建模；不可忽略的缺失协变量；协变量的测量误差，健康结果的稳健混合，以及个体或区域水平传染病统计模型背景下的多种健康结果。忽视数据应用的适当建模（如上所述）可能导致错误的结论，从而对调查抽样和公共卫生产生明显的政策影响。这些发展还将使统计科学的研究人员能够更可靠地拟合和评估他们的假设模型，这对于向公众和决策者报告可靠的结果以更好地规划最终帮助人们是很重要的。我希望在未来五年内培训13名HQP。

In small area estimation (SAE), policy decisions regarding the allocation of resources to sub-groups of a population depend on reliable predictors of their underlying parameters. However, in some sub-groups, called small areas due to small sample sizes relative to the population, the information needed for reliable prediction is typically not available. Consequently, survey (or administrative) data on a coarser scale is used to predict the characteristics of small areas. Mixed models are mainly used to borrow information from alternative sources (e.g., previous surveys, administrative and census data sets) to provide a reliable prediction. Such predictions have many applications, e.g. in disease mapping the main objective is to find reliable rates of disease such as cancer in small areas. It also has other applications in agriculture, economics, policymaking, and allocation of funds. Over the next 5 years, I will continue to develop new and original models in the context of SAE. My plan is to work on 10 projects dealing with non--ignorable missing covariates; quantile responses; robust statistics; measurement error in covariates in longitudinal data; non-parametric responses in the class of generalized linear mixed models. In spatial statistics, I am pursuing research on the analysis of disease rates over space and time. In general, these spatio--temporal models fall under the umbrella of mixed models. The spatio--temporal models are mainly used in disease mapping to provide a reliable estimate of the underlying disease risk by borrowing strength from neighboring geographic sub-regions. The idea behind developments on spatial and spatio--temporal modeling of disease rates is essential to model variations in true rates and better separate systematic variability from random noise, a component that usually overshadows crude rate maps. Over the next 5 years, I will continue to develop new and original spatial and temporal models in my research program. My plan is to work on 9 projects dealing with maximum likelihood estimation (MLE) for complex spatio--temporal models of point- referenced datasets; robust version of the mixture of spatial or spatio--temporal models; MLE for joint modeling of two or more relevant diseases; non--ignorable missing covariates; measurement error in covariates, a robust mixture of health outcome, and multiple health outcomes in the context of the individual- or area -level infectious disease statistical models. Ignoring proper modeling of data applications (as explained above) may lead to wrong conclusions that can have clear policy implications in survey sampling and public health. These developments will also enable researchers in the statistical sciences to engage in more reliable fitting and evaluation of their hypothesized models which are important to report reliable results to the public and policy-makers for better planning to ultimately help people. I expect to train 13 HQP in the next five years.