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

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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.**