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Some of the material in is restricted to members of the community. By logging in, you may be able to gain additional access to certain collections or items. If you have questions about access or logging in, please use the form on the Contact Page.
In this dissertation, we study joint sparsity pursuit and its applications in variable selection in high dimensional data. The first part of dissertation focuses on hierarchical variable selection and its application in a two-way...
In many Monte Carlo applications, one can substitute the use of pseudorandom numbers with quasirandom numbers and achieve improved convergence. This is because quasirandom numbers are more uniform than pseudorandom numbers. The most...
A longitudinal study is a research design that collects observations measured repeatedly from particular individuals over prolonged periods of time. Nowadays, longitudinal studies are widely used in health sciences, social science, ...
In this study, we propose a robust method holding a selective shrinkage power for small area estimation with automatic random effects selection referred to as SARS. In our proposed model, both fixed effects and random effects are treated...
Volatility modeling and forecasting are crucial in risk management and pricing derivatives. High-frequency financial data are dynamic and affected by the microstructure noise. For the univariate case, we define the two-scale realized...
In this dissertation, we develop tools from non-parametric and semi-parametric statistics to perform estimation and inference. In the first chapter, we propose a new method called Non-Parametric Outlier Identification and Smoothing (NOIS...
Count data are ubiquitous in modern statistical applications. How to modeling such data remains a challenging task in machine learning. In this study, we consider various aspects of statistical modeling on Poisson count data. Concerned...
The prediction of financial time series is an essential topic in quantitative investment. In this dissertation, we proposed two types of new models. They are bidirectional encoder representations from Transformers-based financial...
Random numbers are used in a variety of applications including simulation, sampling, and cryptography. Fortunately, there exist many well-established methods of random number generation. An example of a well-known pseudorandom number...
Randomized quasi-Monte Carlo methods have been shown to offer estimates with smaller variances compared with estimates obtained with Monte Carlo. This dissertation examines the application of randomized quasi-Monte Carlo methods in the...
Low-rank matrix approximation is extremely useful in the analysis of data that arises in scientific computing, engineering applications, and data science. However, as data sizes grow, traditional low-rank matrix approximation methods, ...
Multivariate linear models are commonly used for modeling the relationships between multiple responses and covariates. With OLS estimators, one can interpret the results in the analysis. However, the coefficient OLS estimates sometimes...
Bayesian additive regression trees (BART) are a Bayesian machine learning tool for nonparametric function estimation, which has been shown to have outstanding performance in terms of variable selection and prediction accuracy. Unmodified...
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