Advances in Operations Research / 2011 / Article / Tab 2 / Research Article
Outlier-Resistant
𝐿
𝟏
Orthogonal Regression via the Reformulation-Linearization Technique Table 2 Mean of
𝑆
/percentage of instances with
𝑆
≥
0
.
9
for
𝐿
1
OR,
𝐿
2
OR, ppOR-mad, ppOR-qn,
𝜏
-OGK, and PCA-
𝐿
1
with sample sizes
𝑛
=
2
5
, 50, 100, and 200 and contamination levels
𝜖
=
0
.
0
5
,
0
.
1
0
, and 0.25.
Method
𝜖
=
0
.
0
5
𝜖
=
0
.
1
0
𝜖
=
0
.
2
5
𝑛
=
2
5
𝐿
1
OR 0.996/1.000 0.993/1.000 0.680/0.520
𝐿
2
OR 0.981/0.980 0.963/0.920 0.648/0.240 ppOR-mad 0.967/0.900 0.933/0.740 0.859/0.500 ppOR-qn 0.963/0.880 0.944/0.800 0.869/0.460
𝜏
-OGK 0.994/1.000 0.985/0.980 0.842/0.660 PCA-
𝐿
1
0.962/0.940 0.969/0.960 0.794/0.380
𝑛
=
5
0
𝐿
1
OR 0.998/1.000 0.932/0.920 0.602/0.360
𝐿
2
OR 0.988/1.000 0.912/0.860 0.609/0.260 ppOR-mad 0.974/0.900 0.943/0.860 0.903/0.660 ppOR-qn 0.989/1.000 0.962/0.900 0.858/0.400
𝜏
-OGK 0.997/1.000 0.974/0.980 0.818/0.640 PCA-
𝐿
1
0.986/0.960 0.932/0.880 0.779/0.380
𝑛
=
1
0
0
𝐿
1
OR 0.973/0.960 0.931/0.900 0.519/0.180
𝐿
2
OR 0.981/0.960 0.884/0.700 0.623/0.200 ppOR-mad 0.979/0.960 0.956/0.900 0.923/0.700 ppOR-qn 0.989/1.000 0.958/0.900 0.878/0.480
𝜏
-OGK 0.998/1.000 0.977/0.940 0.828/0.540 PCA-
𝐿
1
0.979/0.960 0.940/0.880 0.810/0.340
𝑛
=
2
0
0
𝐿
1
OR 0.932/0.800 0.857/0.760 0.509/0.140
𝐿
2
OR 0.917/0.820 0.805/0.580 0.608/0.160 ppOR-mad 0.975/0.960 0.970/0.920 0.942/0.780 ppOR-qn 0.978/0.980 0.959/0.860 0.893/0.560
𝜏
-OGK 0.997/1.000 0.954/0.920 0.834/0.600 PCA-
𝐿
1
0.926/0.860 0.922/0.820 0.785/0.340
