Small area estimation, and spatial statistics

小区域估计和空间统计模型分别在调查抽样和公共卫生领域具有重要的理论意义和实际意义。近年来，由于对可靠的小面积统计数据的需求不断增长，小面积估计受到了相当大的关注，这些统计数据在制定政策和计划、政府资金分配、区域规划、地方一级的营销决策以及其他用途方面都是必需的。小地区估计的应用领域包括地区一级学龄儿童的贫困人数、小地方的收入、人口普查大都市地区的月失业率以及地方地区与健康有关的估计数。空间统计是指以统计理论为基础的各种技术，其可以识别聚类，比较地理区域之间的比率，将系统模式与随机噪声分离，量化测量的不确定性（例如，估计），并评估空间背景下的潜在预测因素。虽然空间统计对人口和公共卫生特别有用，但这些方法也可以应用于包括天文学，农业和经济学在内的各个领域。 我的建议的特点是发展新的统计方法，将用于说明小面积估计和空间统计模型中发生的变化。在小面积估计中，两个重要的问题，协变量的测量误差和缺失的响应，被认为是在广义线性混合模型的设置，我相信我的新方法，首次提出在这个设置，将有更好的性能比天真的方法。在空间统计学中，在各种泊松混合模型中考虑了多余零计数和协变量测量误差的零膨胀模型：空间，时空和季节调整的时空。在小区域估计和空间统计模型中，我的新方法的性能将在许多真实的应用中进行评估。

Small area estimation and spatial statistical models have practical importance and theoretical interest in survey sampling and public health, respectively. Small area estimation has received considerable attention in recent years due to growing demand for reliable small area statistics that are needed in formulating policies and programs, allocation of government funds, regional planning, marketing decisions at local level, and other uses. Areas of application of small area estimation include poverty counts of school-age children at the area level, income for small places, monthly unemployment rates for Census Metropolitan Areas, and health-related estimates for local areas. Spatial statistics refer to a broad variety of techniques grounded in statistical theory that can identify clusters, compare rates among geographic area, separate systematic patterns from random noise, quantify uncertainty of measures (e.g., estimates), and assess potential predictors in a spatial context. While spatial statistics are particularly useful for population and public health, these methods can also be applied to diverse fields including astronomy, agriculture, and economics. My proposal features the development of new statistical methods that will be used to account the variations occurred in small area estimation and spatial statistical models. In small area estimation, two important issues, measurement errors in covariates and missing responses, are considered in the generalized linear mixed model set up where I believe my new methods, proposed for the first time in this set up, will have better performance than naive methods. In spatial statistics, the zero-inflated model for excess zero counts and measurement error in covariates are considered in various Poisson mixed models: spatial, spatio-temporal and spatio-temporal with seasonal adjustment. In both small area estimation and spatial statistical models, the performance of my new methods will be evaluated in many real applications.