In this dissertation, various aspects of multivariate statistical modeling are discussed. We focus on three important subdivisions of statistics, namely, graphical models, nonparametric regression, and time series analysis. First, probabilistic graphical models are studied in a general setting. Then, in the intersection of graphical models and nonparametric statistics, we introduce a novel regression method (called Iterated Conditional Expectation algorithm) operating on specific graphical models, namely probabilistic DAGs and regression graphs. We describe the technique and prove its (mean-squared) consistency over probabilistic DAGs and regression graphs. Another chapter is devoted to the analysis of regression discontinuity design (RDD), a widely applied pretest-posttest quasi-experimental technique. As a methodological novelty, we propose and discuss a novel alternative method (called jittering RDD) to handle the problem of a discrete running variable in the RDD setting. In the topic of time series analysis, next to some preliminaries, connections of the covariance structure and spectral densities of stationary multidimensional time series are investigated. Based on our theoretical results, a novel dynamic principal component analysis algorithm (called dynPCA) is also introduced. Applications of the introduced methods are also presented.
Some advances in multivariate statistical modeling - PhD public defence
2022. 09. 15. 10:30