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A robust fit for generalized partial linear partial additive models Pan, Yiyang

Abstract

In regression studies, semi-parametric models provide both flexibility and interpretability. In this thesis, we focus on a robust model fitting algorithm for a family of semi-parametric models – the Generalized Partial Linear Partial Addi- tive Models (GAPLMs), which is a hybrid of the widely-used Generalized Linear Models (GLMs) and Generalized Additive Models (GAMs). The traditional model fitting algorithms are mainly based on likelihood proce- dures. However, the resulting fits can be severely distorted by the presence of a small portion of atypical observations (also known as “outliers”), which deviate from the assumed model. Furthermore, the traditional model diag- nostic methods might also fail to detect outliers. In order to systematically solve these problems, we develop a robust model fitting algorithm which is resistant to the effect of outliers. Our method combines the backfitting algorithm and the generalized Speckman estimator to fit the “partial linear partial additive” styled models. Instead of using the likelihood-based weights and adjusted response from the generalized local scoring algorithm (GLSA), we apply the robust weights and adjusted response derived form the robust quasi-likelihood proposed by Cantoni and Ronchetti (2001). We also extend previous methods by proposing a model prediction algorithm for GAPLMs. To compare our robust method with the non-robust one given by the R function gam

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