Nonparametric Statistical Inference for Time Series Trend Analysis, and Statistical Modelling Methods with Applications in Health Research and Environmental Science

我的研究计划侧重于建模时间序列数据与现实世界的应用统计方法。在接下来的五年里，我将专注于时间序列数据的非参数统计推断，以及公共卫生和环境科学中时间序列数据建模的统计建模方法。我的研究结果将为科学家提供新的方法来发现我们的水资源，食物蛋白质加工和气候的趋势，变化和异常，并将导致有效的社会经济干预计划的改进设计。此外，所提出的新的野生动物模拟模型将成为生态学家寻找可持续收获管理系统的有力工具。我的非参数推断研究的目标是开发基于秩或符号的统计方法，用于检测随时间的水平变化，分析时间趋势曲线，并识别集体离群值（不一致）。我感兴趣的秩相关统计，如肯德尔的相关系数，及其各种应用。我最近的工作主要集中在单样本和双样本Wilcoxon型统计。我将继续研究关键问题，即这些统计量的方差扩展。这些非参数方法在环境科学研究中特别有用。最近，这种方法已经被应用于大数据分析中，用于测试变化和检测异常。我将开发趋势测试，重点是高维数据。** 我研究的第二个重点是开发新的统计方法来建模多变量时间序列数据。这一领域的动机是我的工作建模pharmacare配药数据。此类时间序列数据是组成性的，其中每个时间点不同药物类别下的患者比例总和为1，患者人群规模随时间变化。Box和Tiao的时间序列回归方法不再能够直接处理这类数据。我将致力于多变量状态空间方法，以联合建模多变量计数和离散成分。** 我的第三个重点领域是生态学的定量方法。 具体的问题包括野生动物种群重建方法使用年龄在收获时间序列数据。这是因为现实/准确的人口信息通常无法获得。我将使用随机矩阵过程模型来模拟种群和收获数据，并在不同环境条件下估计种群稳定年龄分布。这项工作非常重要，因为收获数据是野生动物生态学研究中最容易获得的数据。* 总的来说，作为一般的统计方法，我提出的程序也适用于科学和社会科学中的许多其他领域，这些领域的数据是复杂的和连续相关的。

My research program focuses on statistical methods for modeling time series data with real-world applications. During the next five years, I will focus on nonparametric statistic inference in time series data, and statistical modelling methods for modeling time series data arising from public health and environmental sciences. The results from my research will provide new ways for scientists to discover trends, changes, and anomalies in our water resources, food protein processes, and climate, and will lead to improved designs for effective socio-economic intervention programs. Additionally, the novel wildlife simulation model proposed will become a powerful tool for ecologists to search for the sustainable harvest management system.******The objective of my nonparametric inference research, is to develop rank- or sign-based statistic methods for detecting level shifts over time, analyzing temporal trend profiles, and identifying collective outliers (discords). I am interested in rank-correlation statistics, such as Kendall's correlation coefficient, and its various applications. My recent work has focused on one- and two-sample Wilcoxon type statistics. I will continue to work on the key issue, the variance expansion of these statistics. These nonparametric methods are particularly useful in environmental science research. Recently, such methods have been adapted to be used in big data analytics for testing change and detecting anomalies. I will develop trend tests with an emphasis on high dimensional data. ******A second focus of my research is to develop novel statistical methods for modeling multivariate times series data. This area has been motivated by my work modelling pharmacare dispensation data. Such time series data are compositional where the proportions of patients under various drug categories at each time point sum to 1 and the patient population size is changing over time. The Box and Tiao's time series regression method is no longer able to directly address this kind of data. I will work on multivariate state-space approaches to jointly modelling multivariate counts and discrete compositions. ******My third area of focus is in the area of quantitative methods for ecology. The specific problem includes wildlife population reconstruction methods using age-at-harvest time series data. This is due to the fact that realistic/accurate population information is generally unavailable. I will use stochastic matrix process models to simulate both population and harvest data, and to enable the estimation of the population stable age distribution in different environmental conditions. This work is very important since the harvest data are the most accessible data in wildlife ecology research. ******Overall, as general statistical methodologies, my proposed procedures are also applicable in many other areas within science and social sciences where the data are complex and serially correlated.**