Significance Levels in Exploratory Projection Pursuit
针对投影追踪方法，推导了弗里德曼投影追踪指数P值的理论近似公式，并与蒙特卡洛模拟结果比较，帮助判断高维数据中的结构是否真实。
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.