Significance Levels in Exploratory Projection Pursuit
J. Sun · Biometrika · 1991
In exploratory data analysis, projection pursuit methods explore the ‘nonlinear’ structure of high dimensional data. It is useful to have a significance test to help us decide whether apparent structure is real or just the effect of noise. Monte Carlo methods can be helpful to achieve this, but, unfortunately, in this case they are computationally expensive. In this paper, under a suitable null hypothesis, we derive a theoretical approximation for the P value associated with Friedman's projection pursuit index (Friedman, 1987). The result of Monte Carlo simulations is compared with our analytical result. Some practical aspects are discussed.