Statistical Models Commons^™

Sparse Model Selection Using Information Complexity, Yaojin Sun

Doctoral Dissertations

This dissertation studies and uses the application of information complexity to statistical model selection through three different projects. Specifically, we design statistical models that incorporate sparsity features to make the models more explanatory and computationally efficient.

In the first project, we propose a Sparse Bridge Regression model for variable selection when the number of variables is much greater than the number of observations if model misspecification occurs. The model is demonstrated to have excellent explanatory power in high-dimensional data analysis through numerical simulations and real-world data analysis.

The second project proposes a novel hybrid modeling method that utilizes a mixture …

Beta Mixture And Contaminated Model With Constraints And Application With Micro-Array Data, Ya Qi

Theses and Dissertations--Statistics

This dissertation research is concentrated on the Contaminated Beta(CB) model and its application in micro-array data analysis. Modified Likelihood Ratio Test (MLRT) introduced by [Chen et al., 2001] is used for testing the omnibus null hypothesis of no contamination of Beta(1,1)([Dai and Charnigo, 2008]). We design constraints for two-component CB model, which put the mode toward the left end of the distribution to reflect the abundance of small p-values of micro-array data, to increase the test power. A three-component CB model might be useful when distinguishing high differentially expressed genes and moderate differentially expressed genes. If the null hypothesis above …

Information Metrics For Predictive Modeling And Machine Learning, Kostantinos Gourgoulias

Doctoral Dissertations

The ever-increasing complexity of the models used in predictive modeling and data science and their use for prediction and inference has made the development of tools for uncertainty quantification and model selection especially important. In this work, we seek to understand the various trade-offs associated with the simulation of stochastic systems. Some trade-offs are computational, e.g., execution time of an algorithm versus accuracy of simulation. Others are analytical: whether or not we are able to find tractable substitutes for quantities of interest, e.g., distributions, ergodic averages, etc. The first two chapters of this thesis deal with the study of the …

Variable Selection In Single Index Varying Coefficient Models With Lasso, Peng Wang

Doctoral Dissertations

Single index varying coefficient model is a very attractive statistical model due to its ability to reduce dimensions and easy-of-interpretation. There are many theoretical studies and practical applications with it, but typically without features of variable selection, and no public software is available for solving it. Here we propose a new algorithm to fit the single index varying coefficient model, and to carry variable selection in the index part with LASSO. The core idea is a two-step scheme which alternates between estimating coefficient functions and selecting-and-estimating the single index. Both in simulation and in application to a Geoscience dataset, we …

Seasonal Decomposition For Geographical Time Series Using Nonparametric Regression, Hyukjun Gweon

Electronic Thesis and Dissertation Repository

A time series often contains various systematic effects such as trends and seasonality. These different components can be determined and separated by decomposition methods. In this thesis, we discuss time series decomposition process using nonparametric regression. A method based on both loess and harmonic regression is suggested and an optimal model selection method is discussed. We then compare the process with seasonal-trend decomposition by loess STL (Cleveland, 1979). While STL works well when that proper parameters are used, the method we introduce is also competitive: it makes parameter choice more automatic and less complex. The decomposition process often requires that …