基于改进鲁棒马氏距离与卡平方分布的粗差判别及其应用

Outliers Detection Based on Modified Robust-mahalanobis-distance and Chi-squared Distribution and Its Application

针对可能含有粗差的样本数据,提出一种基于改进鲁棒马氏距离和卡平方分布的粗差判别方法。首先,该算法通过CDC2-MVT(Closest distance to center-Ellipsoidal multivariate trimming)初步抗差估计样本的鲁棒马氏距离,接着通过CESD(Consistently estimate the standard deviation)渐近估计鲁棒马氏距离的标准差,从而找出最一致的观测样本。然后,基于最一致的观测样本重新估计总体的位置参数和尺度参数,进而估计改进鲁棒马氏距离,在保证估计位置参数和尺度参数抗差性的同时,克服了CDC2-MVT方法效率不足的缺点。最后,基于改进鲁棒马氏距离,通过卡平方分布判别样本数据中的粗差。仿真研究与实际应用表明,提出的粗差判别方法明显优于基于CDC2-MVT、CDCm-MVT和MCD的粗差判别方法。

A new way of outlier detection based on modified robust mahalanobis-distance and Chi-squared distribution was proposed aiming at that samples may include outliers. Fii＇stly, estimated the mahalanobis-distance preliminarily by means of CDC2-MVT. Secondly, estimated the standard deviation of the robust mahalanobis-distance to find the most consistent observations through process of CESD. Then,used the most consistent observations to re-estimate the location and scale parameter and further estimated the modified robust mahalanobis-distance which was still robust to outlier in the mean time when overcomes the drawback of CDC2-MVT that lacks efficiency. Lastly, detected the outlier from the modified robust mahalanobis-distance by means of Chi-square distribution. Simulated experiments and real applications show that the proposed way of outlier detection performs better than CDC2-MVT,CDCm-MVT and MCD method.