The goal of this dissertation is to develop some classical limit theorems for the additive functionals of the homogeneous Markov chains in the special class of the so-called, Loop Markov Chains. The additive functionals of the Markov chains have t...
In this dissertation, the classic one dimension orthogonal wavelet construction scheme is discussed and extended to construct Parseval's frame wavelets in high dimension scenario. An iterative algorithm is developed to construct various Parseval's...
Competing risks often arise where more than one event compete with each other for a subject. The cumulative incidence function is a proper summary quantity for analyzing competing risks data. In epidemiologic cohort studies, case-cohort study desi...
In financial time series nonlinear effects and time-varying effects are observed. In this dissertation we propose a predictive regression model with time varying coefficients and functional coefficients. It allows for nonstationary predictors. We establi...
The design basis functions in IGA are refined and enhanced by extra enrichment functions and various local refinements with the use of partition of unity (PU) functions with flat-top. These reconditioned and modified basis functions are pushed for...
