Statistical Analysis of Complex Featured Data: High Dimensionality, Measurement Error and Missing Values

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As the advancement of modern technology in acquiring data, data with diverse features are becoming more accessible than ever before. The increasing complexity of structures and the large dimension of data have posed an urgent need for the development of novel and flexible modeling and analysis tools. While many complex features may be present in different applications, this research focuses on two prevailing issues commonly present in modern data : the quality and dimensionality of data. I plan to explore important problems in the following areas. (1) High dimensional data with measurement error and missing values In the era of Big Data, large scale data are often available where the dimension of the variables is much larger than the number of subjects in the study. This presents a great challenge to traditional statistical methods which normally require the sample size to be bigger than the dimension of the variables. In addition, we face challenges related to data quality - measurement imprecision and missing observations. This research aims to investigate problems concerning high dimensionality, measurement error, and missing observations. The plan is to examine how measurement error and missing values may interplay in the analysis of high dimensional data. The objectives are to develop valid inference methods to handle data with all these features involved. Applications of the developed methods to survival data, image data and longitudinal data are planned. (2) Causal inference with complex featured data As opposed to association studies, causal inference is often the focus of empirical research. While many research methods are available for various settings, they are vulnerable to poor quality data. Most existing methods require that the data are “perfect” in the sense that no missing observations nor measurement error are present, but these assumptions are often violated in practice. Measurement error and missing observations have been a long standing concern in many studies including epidemiological, nutrition and environmental studies. However, research on causal inference with these features is rather limited and remains unexplored. I plan to explore this exciting area and develop new methods to address complex effects caused by measurement error and/or missing observation on causal inference. Furthermore, I intend to investigate the problems in the presence of large scale data where the dimension of potential confounders is high. My primary goals are to develop original and innovative methodology in advancing foundational work and to facilitate applications. This research is anticipated to provide valuable insights into making the best use of available large scale data and to broaden the scope of existing strategies and research. It is expected to have significant impact on the statistical community as well as other fields including public health, medical studies and data science.