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Parametric regression fits curves to data using parametric families: for example, lines, parabolas and exponentials. Nonparametric regression requires only that the curve be smooth with shape depending primarily upon the data. Semiparametric regression combines nonparametric and parametric models. For example, when analyzing mortality and air pollution, pollution effects are commonly modeled linearly, and confounders such as time, temperature and humidity nonparametrically. There are many methods for nonparametric estimation including local polynomial regression, smoothing splines, and wavelets. However, penalized splines have a number of convenient features:
- ease of use
- modularity, meaning components of the model can be developed separately
- close connections with parametric statistics, e.g., maximum likelihood and likelihood ratio tests
- ability to implement with standard software, e.g., SAS, R, and WinBUGS
The course will focus on semiparametric models based on penalized splines viewed as linear or generalized linear mixed models. Topics include
- scatterplot smoothing
- penalized splines as best linear unbiased predictors
- automatic selection of the degree of smoothing, especially by restricted maximum likelihood
- additive models
- inference
- generalized semiparametric regression
- spatial statistics
- measurement error
- Bayesian semiparametric regression
- programming in SAS, S-PLUS and WinBUGS.
OPTIONAL TEXTBOOK AVAILABLE
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= Applied Session,
= Theme Session,
= Presenter