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

时间序列趋势分析的非参数统计推断以及在健康研究和环境科学中应用的统计建模方法

• 批准号: RGPIN-2018-05578
• 负责人: Zhang, Ying
• 金额: $ 1.31万
• 依托单位: Acadia University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=759190
• 关键词: Nonparametric; Statistical; Inference; Time; Series

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.

我的研究项目侧重于利用实际应用对时间序列数据进行建模的统计方法。在接下来的五年中，我将重点研究时间序列数据中的非参数统计推断，以及对公共卫生和环境科学中产生的时间序列数据进行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、食品蛋白质过程和气候的趋势、变化和异常，并将改进有效的社会经济干预计划的设计。此外，提出的新颖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。我的非参数推理研究的目标是开发基于等级或符号的统计方法来检测随时间变化的水平变化，分析时间趋势概况，并识别集体异常值（不一致）。我对等级相关统计感兴趣，例如肯德尔相关系数及其各种应用。我最近的工作重点是一样本和二样本 Wilcoxon 类型统计。我将继续研究关键问题，即这些统计数据的方差扩展。这些非参数方法在环境科学研究中特别有用。最近，此类方法已适用于大数据分析，以测试变化和检测异常。我将开发趋势测试，重点关注高维数据。我研究的第二个重点是开发新的统计方法来建模多元时间序列数据。我对药物配药数据进行建模的工作推动了这一领域的发展。此类时间序列数据是组合数据，其中每个时间点不同药物类别下的患者比例之和为 1，并且患者群体规模随时间变化。 Box和Tiao的时间序列回归方法不再能够直接处理这类数据。我将研究多元状态空间方法来联合建模多元计数和离散组合。我的第三个重点领域是生态学定量方法领域。 具体问题包括使用收获年龄时间序列数据的野生动物种群重建方法。这是因为通常无法获得现实/准确的人口信息。我将使用随机矩阵过程模型来模拟种群和收获数据，并能够估计不同环境条件下种群稳定的年龄分布。这项工作非常重要，因为收获数据是野生动物生态研究中最容易获得的数据。总体而言，作为一般统计方法，我提出的程序也适用于数据复杂且连续相关的科学和社会科学的许多其他领域。