Mixture of functional linear models and its application to CO2-GDP functional data

Functional linear models are important tools for studying the relationship between functional response and covariates. However, if subjects come from an inhomogeneous population that demonstrates different linear relationship between the response and covariates among different subpopulations/clusters, a single functional linear model is no longer adequate for the data. A new class of mixtures of functional linear models for the analysis of heterogeneous functional data is introduced. Identifiability is established for the proposed class of mixture models under mild conditions. The proposed estimation procedures combine the ideas of local kernel regression, functional principal component analysis and EM algorithm. A generalized likelihood ratio test based on a conditional bootstrap is given as to whether the regression coefficient functions are constant. A Monte Carlo simulation study is conducted to examine the finite sample performance of the new methodology. Finally, the analysis of CO2-GDP data reveals the dynamic patterns of relationship between CO2 and GDP among different countries

Mixture of functional linear models and its application to CO2-GDP functional data

Functional linear models are important tools for studying the relationship between functional response and covariates. However, if subjects come from an inhomogeneous population that demonstrates different linear relationship between the response and covariates among different subpopulations/clusters, a single functional linear model is no longer adequate for the data. A new class of mixtures of functional linear models for the analysis of heterogeneous functional data is introduced. Identifiability is established for the proposed class of mixture models under mild conditions. The proposed estimation procedures combine the ideas of local kernel regression, functional principal component analysis and EM algorithm. A generalized likelihood ratio test based on a conditional bootstrap is given as to whether the regression coefficient functions are constant. A Monte Carlo simulation study is conducted to examine the finite sample performance of the new methodology. Finally, the analysis of CO2-GDP data reveals the dynamic patterns of relationship between CO2 and GDP among different countries

Advanced Statistical Learning Techniques for High-Dimensional Imaging Data

With the rapid development of neuroimaging techniques, scientists are interested in identifying imaging biomarkers that are related to different subtypes or transitional stages of various cancers, neuropsychiatric diseases, and neurodegenerative diseases. Scalar-on-image models have been proven to demonstrate good performance in such tasks. However, due to their high dimensionality, traditional methods may not work well in the estimation of such models. Some existing penalization methods may improve the performance but fail to take the complex spatial structure of the neuroimaging data into account. In the past decade, the spatially regularized methods have been popular due to their good performance in terms of both estimation and prediction. Despite the progress, many challenges still remain. In particular, most existing image classification methods focus on binary classification and consequently may underperform for the tasks of classifying diseases with multiple subtypes or transitional stages. Moreover, neuroimaging data usually present significant heterogeneity across subjects. As a result, existing methods for homogeneous data may fail. In this dissertation, we investigate several new statistical learning techniques and propose a Spatial Multi-category Angle based Classifier (SMAC), a Subject Variant Scalar-on-Image Regression (SVSIR) model and a Masking Convolutional Neural Network (MCNN) model to address the above issues. Extensive simulation studies and practical applications in neuroscience are presented to demonstrate the effectiveness of our proposed methods.Doctor of Philosoph