Description
Regression is one of the most common problems in Statistics. In the most simple case, in simple linear regression, one has bivariate data pairs (x_i,y_i) and tries to fit a line of type y=a+bx through the data. However, the actual relationship between predictor and response is often far from linear, in which case linear regression methods are then inadequate. To some extent, one can solve this problem by employing alternative parametric functions, e.g. a parabola, but these models are not very flexible and require a large number of parameters if the data structure is quite complex.The better approach in those cases is to use nonparametric regression methods, which allow for arbitrary 'smooth' functions and do not require to predefine a parametric regression function. As these methods summarize the data by a smooth curve, they are often referred to as 'smoothing' methods. Today exist a large number of well established smoothing methods, most of them based on either `kernels' or `splines', which find frequent application in all kind of disciplines, e.g. natural and environmental sciences, actuarial sciences, and medicine. Some examples for smooth regression curves are given in the images to the right (top: fitted curve for a univariate regression problem; bottom: fitted surface for a bivariate regression problem).
In this project you will learn how smoothing techniques work, get some insight into their theoretical background, and apply them on real data sets using modern statistical software packages (e.g. R). More advanced techniques, such as logistic additive models as used in classification problems, can be considered depending on interest.
Prerequisites
- Statistical Concepts II
Resources
- James G., Witten D., Hastie T., and Tibshirani R. (2013) Introduction to Statistical Learning. Springer, New York. PDF , Section 7.
- Hastie T., Tibhsirani R., and Friedman, J. (2001) The Elements of Statistical Learning. Springer, New York. PDF , Sections 5.1-5.5 and 6.
Examples
