Ultrahigh‐dimensional generalized additive model: Unified theory and methods

Partly parametric generalized additive model

In many scientific studies, the response variable bears a generalized nonlinear regression relationship with a certain covariate of interest, which may, however, be confounded by other covariates with unknown functional form. We propose a new class of models, the partly parametric generalized additive model (PPGAM) for doing generalized nonlinear regression with the confounding covariate effect...

Multirate generalized additive Runge Kutta methods

This work constructs a new class of multirate schemes based on the recently developed generalized additive Runge-Kutta (GARK) methods [10]. Multirate schemes use different step sizes for different components and for different partitions of the right-hand side based on the local activity levels. We show that the new multirate GARK family includes many well-known multirate schemes as special case...

Fourier Analytic Methods in Additive Number Theory

In recent years, analytic methods have become prominent in additive number theory. In particular, finite Fourier analysis is well-suited to solve some problems that are too difficult for purely combinatorial techniques. Among these is Szemerédi’s Theorem, a statement regarding the density of integral sets and the existence of arithmetic progressions in those sets. In this thesis, we give a gene...

Improving Credit Scoring by Generalized Additive Model

Logistic Regression has been widely used in the financial service industry for credit scoring models. Despite its advantages in easy interpretation and low computing cost, Logistic Regression is under the criticism of failure to model the nonlinear features of the predictors effect on the dependent variable and therefore might lead to unsatisfactory results. Modern statistical techniques such a...

Definable additive categories: purity and model theory