摘要
将小误差和粗差看成同一正态分布时 ,最小二乘估计不抗差 ,而其和极大似然估计是抗差的 ,其统计性质受尺度因子 (方差因子 ) k影响。k =1 .41 6时 ,有最小最大偏差 ,即最强的抗差能力 ,效率为 83.85 ;k=2 .73时 ,其最大偏差不超过无粗差时 (以 2倍中误差为阈值 )最小二乘估计的最大偏差 ,具有很好的抗差性 ,效率为 97.91 ,是最合适的取值 ;k =∞时 。
When small errors and gross errors are regarded as of the same normal distribution,the LS method is blunderirresistant.However the sum maximal likelihood estimation is blunderresistant. Its properties rely on the scale factor k. The minimal maximal deviaton is at k= 1.416 ,whose ability to resist gross errors is the strongest,its efficiency is 83.85%;When k is 2.73,the maximal deviation is not more than that of the LS estimation. Without any gross error,the blunderresistance is good,the efficiency is 97.91%,so the “k=2.73” is the most fitable.When k=∞,the sum maximal likelihood method is equal to the LS method.
出处
《地壳形变与地震》
CSCD
2000年第3期33-38,共6页
Crustal Deformation and Earthquake
基金
广西自然科学基金资助项目 !编号 :9912 0 0 8
关键词
数据处理
和极大似然估计
正态分布
测量
误差
data processing, the sum maximal likelihood estimation, normal distribution, efficiency
