Influence Analysis of Nongaussianity by Applying Projection Pursuit

• Main Authors: Chin-Zen Cheng, 鄭清仁
• Other Authors: none
• Format: Others
• Language: en_US
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/53766687957568781608

碩士 === 國立中正大學 === 統計科學所 === 94 === Gaussian distribution is the least structured from the information-theoretic point of view. In this thesis, the projection pursuit is performed by finding the most nongaussian projection to explore the clustering structure of the data. We use kurtosis as a measure of nongaussianity to find the projection direction. Kurtosis is well known to be sensitive to abnormal observations, henceforth the projection direction will be essentially affected by unusual points. The perturbation theory provides a useful tool in sensitivity analysis. In this thesis, we develop influence functions for the projection direction to investigate the influence of unusual observations. It is well-known that single-perturbation diagnostics can suffer from the masking effect. Hence we also develop the pair-perturbation influence functions to detect the masked influential points and outliers. A simulated data and a specific data example are provided to illustrate the applications of these approaches.