A Study On Robust Multivariable Statistical Analysis Method And Algorithm Realization

Traditional multivariable analysis method mainly includes Principal component analysis method , Factor analysis method that we usually talk of . The commons among those methods is that all of them calculate the mean vector and the covariance matrix of sample then calculate other variables by using them. When there is no outlier in the sample, these methods can get good result. But when the sample includes outliers, these methods are easily affected by them. Because Traditional mean vector and covariance matrix are not robust estimator, this dissertation combines ideas of robust statistics with multivariable analysis method from robust statistics aspect. Base on the study of current robust multivariable analysis methods, some algorithms of robust multivariable analysis methods which are used often are introduced . By using one of them, some robust multivariable outlier detection methods are built. This dissertation focus on the study of the most popular FAST-MCD method which is improved by concentrating on its shortcoming, constructs robust mean vector and robust covariance matrix which is applied in Principal component analysis method and Factor analysis. Besides that, the calculation of robust leverage point and robust factor analysis are put forward. From the result of simulation and empirical study , the improved method and the new robust estimator are good for resisting outliers, decreasing their influence greatly. Finally the FAST-MCD algorithm is realized in EXCEL, which is friendly to be used.