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Varying Coefficient Regression Models: A Review and New Developments
Author(s) -
Park Byeong U.,
Mammen Enno,
Lee Young K.,
Lee Eun Ryung
Publication year - 2015
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/insr.12029
Subject(s) - interpretability , smoothing , covariate , curse of dimensionality , linear regression , regression , mathematics , regression analysis , additive model , component (thermodynamics) , nonparametric regression , econometrics , computer science , data mining , statistics , machine learning , physics , thermodynamics
Summary 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.