Effects of Numerical Errors on Sample Mahalanobis Distances
Effects of Numerical Errors on Sample Mahalanobis Distances
复制标题
数值误差对样本马氏距离的影响
DOI：
10.1587/transinf.2015edp7348
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Yasuyuki Kobayashi
中科院分区：
文献类型：
--
作者：
Yasuyuki Kobayashi
研究了样本马氏距离（T2 = y ′ S（cid：0）1 y）与样本协方差矩阵S的数值误差.发现为了抑制T2的数值误差，需要萨蒂斯下列条件：艾德.第一，S的条件数的平方根倒数应大于计算临界点实数变量的相对误差。第二个提出的条件是基于T2中观测样本向量y的相对误差。如果y的相对误差大于实数变量的相对误差，则前者决定T2的数值误差。数值实验表明，满足上述两个条件，T2的数值误差可以得到抑制，艾德.
SUMMARY The numerical error of a sample Mahalanobis distance ( T 2 = y ′ S (cid:0) 1 y ) with sample covariance matrix S is investigated. It is found that in order to suppress the numerical error of T 2 , the following condi- tions need to be satisfied. First, the reciprocal square root of the condition number of S should be larger than the relative error of calculating floating- point real-number variables. The second proposed condition is based on the relative error of the observed sample vector y in T 2 . If the relative er- ror of y is larger than the relative error of the real-number variables, the former governs the numerical error of T 2 . Numerical experiments are con- ducted to show that the numerical error of T 2 can be suppressed if the two above-mentioned conditions are satisfied.