Computational Statistics is the area of specialization within statistics that includes statistical visualization and other computationally-intensive methods of statistics for mining large, nonhomogeneous, multi-dimensional datasets so as to discover knowledge in the data. As in all areas of statistics, probability models are important, and results are qualified by statements of confidence or of probability. An important activity in computational statistics is model building and evaluation.
First, the basic multiple linear regression is reviewed. Then, some nonparametric procedures for regression and classification are introduced and explained. In particular, Kernel estimators, smoothing splines, classification and regression trees, additive models, projection pursuit and eventually neural nets will be considered, where some of them have a straightforward interpretation, other are useful for obtaining good predictions.
The main problems arising in computational statistics like the curse of dimensionality will be discussed. Moreover, the goodness of a given (complex) model for estimation and prediction is analyzed using resampling, bootstrap and cross-validation techniques.
