Varying Coefficient Regression Models: A Review and New Developments

• Published in: International statistical review Vol. 83; no. 1; pp. 36 - 64
• Main Authors: Park, Byeong U., Mammen, Enno, Lee, Young K., Lee, Eun Ryung
• Format: Journal Article
• Language: English
• Published: Hoboken Blackwell Publishing Ltd 01.04.2015; Blackwell Publishing; John Wiley & Sons, Inc
• Subjects: Coefficients; Dimensional analysis; Estimating; integral equation; kernel smoothing; longitudinal data; Mathematical models; Parameter estimation; partially linear models; penalised likelihood methods; projection; quasi-likelihood; Regression; Regression analysis; robust estimation; shrinkage estimation; sieve estimation; Smoothing; Topology; Varying coefficient models
• ISSN: 0306-7734; 1751-5823
• DOI: 10.1111/insr.12029

Varying coefficient regression models are known to be very useful tools for analysing the relation between a response and a group of covariates. Their structure and interpretability are similar to those for the traditional linear regression model, but they are more flexible because of the infinite dimensionality of the corresponding parameter spaces. The aims of this paper are to give an overview on the existing methodological and theoretical developments for varying coefficient models and to discuss their extensions with some new developments. The new developments enable us to use different amount of smoothing for estimating different component functions in the models. They are for a flexible form of varying coefficient models that requires smoothing across different covariates' spaces and are based on the smooth backfitting technique that is admitted as a powerful technique for fitting structural regression models and is also known to free us from the curse of dimensionality.