Table 1 Hocking data set diagnostics
From: On studentized residuals in the quantile regression framework
ESs corresponding to RQs | \(\tau\) | MAD (16) | \({{\upsilon }_{(i)J_\tau }}\) (14) | |||
|---|---|---|---|---|---|---|
8 | \(11^{\triangle }\) | 16 | \(18^{\triangle }\) | 0.0853 | None | \(17^+({1.789}^{*})\) |
8 | \(11^{\triangle }\) | 16 | 19 | 0.0930 | None | \(17^+({2.043}^{*})\) |
8 | 11 | 19 | \(24^{\times }\) | 0.1232 | None | \(17^+({2.406}^{*})\) |
8 | 12 | 13 | \(24^{\times }\) | 0.1861 | \(17^+({3.645}^{**})\), \(18^{\triangle }({-4.582}^{**})\) | \(17^+({1.822}^{*})\), \(18^{\triangle }({-6.507}^{**})\) |
8 | 13 | 14 | \(24^{\times }\) | 0.2046 | \(11^{\triangle }({ -4.060}^{**})\), \(17^+({5.022}^{**})\), \(18^{\triangle }({-7.486}^{**})\) | \(17^+({2.460}^{*})\), \(18^{\triangle }({-4.869}^{**})\) |
1 | 14 | \(24^{\times }\) | 26 | 0.2528 | \(11^{\triangle }({ -4.060}^{**})\), \(17^+({5.022}^{**})\), \(18^{\triangle }({-7.486}^{**})\) | \(17^+({2.315}^{*})\), \(18^{\triangle }({-5.439}^{**})\) |
1 | 5 | 14 | \(24^{\times }\) | 0.2593 | \(11^{\triangle }({ -4.066}^{**})\), \(17^+({5.022}^{**})\), \(18^{\triangle }({-7.494}^{**})\) | \(17^+({2.315}^{*})\), \(18^{\triangle }({-5.439}^{**})\) |
1 | 14 | 16 | \(24^{\times }\) | 0.3053 | \(11^{\triangle }({ -5.495}^{**})\), \(17^+({6.099}^{**})\), \(18^{\triangle }({-9.149}^{**})\) | \(17^+({1.977}^{*})\), \(18^{\triangle }({-6.853}^{**})\) |
1 | 4 | 16 | \(24^{\times }\) | 0.3659 | \(11^{\triangle }({ -6.205}^{**})\), \(17^+({6.462}^{**})\), \(18^{\triangle }({-10.647}^{**})\) | \(17^+({2.246}^{*})\), \(18^{\triangle }({-6.394}^{**})\) |
1 | 14 | 23 | \(24^{\times }\) | 0.4018 | \(11^{\triangle }({ -6.205}^{**})\), \(17^+({6.462}^{**})\), \(18^{\triangle }({-10.647}^{**})\) | \(17^+({2.241}^{*})\), \(18^{\triangle }({-6.394}^{**})\) |
14 | 16 | 23 | \(24^{\times }\) | 0.4412 | \(11^{\triangle }({ -6.822}^{**})\), \(17^+({6.920}^{**})\), \(18^{\triangle }({-11.740}^{**})\) | \(17^+({1.871}^{*})\),\(18^{\triangle }({-7.223}^{**})\) |
10 | 14 | 16 | \(24^{\times }\) | 0.4686 | \(11^{\triangle }({ -6.602}^{**})\), \(17^+({6.437}^{**})\), \(18^{\triangle }({-11.162}^{**})\) | \(17^+({2.143}^{*})\), \(18^{\triangle }({-5.689}^{**})\) |
7 | 10 | 14 | \(24^{\times }\) | 0.5370 | \(11^{\triangle }({ -6.502}^{**})\), \(17^+({6.277}^{**})\), \(18^{\triangle }({-10.923}^{**})\) | \(11^{\triangle }({ -1.741}^{*})\), \(17^+({2.073}^{*})\), \(18^{\triangle }({-5.689}^{**})\) |
3 | 9 | 10 | \(24^{\times }\) | 0.5448 | \(11^{\triangle }({ -6.728}^{**})\), \(17^+({6.290}^{**})\),\(18^{\triangle }({-11.073}^{**})\) | \(11^{\triangle }({ -1.741}^{*})\), \(17^+({2.073}^{*})\), \(18^{\triangle }({-5.689}^{**})\) |
3 | 8 | 10 | \(24^{\times }\) | 0.5512 | \(11^{\triangle }({ -6.728}^{**})\), \(17^+({6.290}^{**})\), \(18^{\triangle }({-11.073}^{**})\) | \(17^+({1.893}^{*})\), \(18^{\triangle }({-6.350}^{**})\) |
8 | 9 | 10 | \(24^{\times }\) | 0.6215 | \(11^{\triangle }({ -7.205}^{**})\), \(17^+({6.045}^{**})\), \(18^{\triangle }({-11.492}^{**})\) | \(17^+({2.013}^{*})\), \(18^{\triangle }({-4.843}^{**})\) |
8 | 9 | \(24^{\times }\) | 25 | 0.6315 | \(11^{\triangle }({ -7.205}^{**})\), \(17^+({6.045}^{**})\), \(18^{\triangle }({-11.492}^{**})\) | \(11^{\triangle }({ -2.301}^{**})\), \(17^+({2.704}^{**})\), \(18^{\triangle }({-2.543}^{**})\) |
9 | 15 | \(24^{\times }\) | 25 | 0.6839 | \(11^{\triangle }({ -7.224}^{**})\), \(17^+({5.986}^{**})\), \(18^{\triangle }({-11.488}^{**})\) | \(11^{\triangle }({ -2.132}^{**})\), \(17^+({2.102}^{**})\), \(18^{\triangle }({-4.229}^{**})\) |
8 | 9 | 15 | \(24^{\times }\) | 0.7227 | \(11^{\triangle }({ -7.240}^{**})\), \(17^+({5.971}^{**})\), \(18^{\triangle }({-11.476}^{**})\) | \(18^{\triangle }({-6.832}^{**})\) |
8 | 10 | 15 | \(24^{\times }\) | 0.7304 | \(11^{\triangle }({ -7.240}^{**})\), \(17^+({5.971}^{**})\), \(18^{\triangle }({-11.476}^{**})\) | \(18^{\triangle }({-6.832}^{**})\) |
6 | 8 | 21 | \(24^{\times }\) | 0.7385 | \(11^{\triangle }({ -7.240}^{**})\), \(17^+({5.971}^{**})\), \(18^{\triangle }({-11.476}^{**})\) | \(11^{\triangle }({ -1.911}^{*})\), \(18^{\triangle }({-4.510}^{**})\) |
6 | 21 | 22 | \(24^{\times }\) | 0.7660 | \(11^{\triangle }({ -6.866}^{**})\), \(17^+({4.990}^{**})\), \(18^{\triangle }({-10.409}^{**})\) | \(11^{\triangle }({ -2.236}^{*})\), \(17^+({2.020}^{*})\), \(18^{\triangle }({-2.687}^{*})\) |
6 | 8 | 22 | \(24^{\times }\) | 0.8276 | \(11^{\triangle }({ -5.260}^{**})\), \(17^+({3.564}^{**})\), \(18^{\triangle }({-7.887}^{**})\) | \(11^{\triangle }({ -2.807}^{*})\), \(17^+({1.908}^{*})\), \(18^{\triangle }({-2.526}^{*})\) |
2 | 6 | 8 | \(24^{\times }\) | 0.9549 | None | \(11^{\triangle }({ -2.078}^{*})\), \(18^{\triangle }({-3.067}^{**})\) |
6 | 8 | 16 | \(24^{\times }\) | 0.9570 | \(11^{\triangle }({ -2.184}^{**})\), \(18^{\triangle }({-2.897}^{**})\) | \(11^{\triangle }({ -2.078}^{*})\), \(18^{\triangle }({-3.067}^{**})\) |