It is generally accepted that training in statistics must include
some exposure to the mechanics of computational statistics. This exposure
to computational methods is of an essential nature when we consider extremely
high dimensional data. Computer aided techniques can help us discover
dependencies in high dimensions without complicated mathematical
tools. A draftman's plot (i.e., a matrix of pairwise scatterplots like
in Figure 1.14) may lead us immediately to a theoretical
hypothesis (on a lower dimensional space) about the relationship
of the variables.
Computer aided techniques are therefore at the heart of multivariate
18. Highly Interactive, Computationally Intensive Techniques
In this chapter we first present the concept of Simplicial Depth--a
multivariate extension of the data depth concept of Section 1.1.
We then present Projection Pursuit--a semiparametric technique which
is based on a one-dimensional, flexible regression or
on the idea of density smoothing applied to
PCA type projections. A similar model is underlying the Sliced
Inverse Regression (SIR) technique which we discuss in Section 18.3.