Draft

Quantile Models

QTE

The results are based on a location-scale model as described the corresponding Example with \(5000\) observations.

The non-uniform results (coverage, ci length and bias) refer to averaged values over all quantiles (point-wise confidende intervals).

DoubleML Version                       0.9.0
Script                        pq_coverage.py
Date                     2024-09-09 12:24:40
Total Runtime (seconds)         18061.192513
Python Version                        3.12.5
Table 1: Coverage for 95.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage Uniform CI Length Uniform Coverage
LGBM LGBM 0.155 0.736 0.941 1.031 0.910
LGBM Logistic Regression 0.122 0.507 0.908 0.714 0.840
Logistic Regression LGBM 0.159 0.749 0.948 1.029 0.920
Logistic Regression Logistic Regression 0.124 0.518 0.912 0.720 0.860
Table 2: Coverage for 90.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage Uniform CI Length Uniform Coverage
LGBM LGBM 0.155 0.618 0.882 0.934 0.850
LGBM Logistic Regression 0.122 0.426 0.830 0.646 0.780
Logistic Regression LGBM 0.159 0.629 0.896 0.931 0.870
Logistic Regression Logistic Regression 0.124 0.434 0.843 0.647 0.810

Potential Quantiles

Y(0) - Quantile

Table 3: Coverage for 95.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage
LGBM LGBM 0.149 0.692 0.935
LGBM Logistic Regression 0.114 0.460 0.886
Logistic Regression LGBM 0.151 0.701 0.942
Logistic Regression Logistic Regression 0.112 0.464 0.902
Table 4: Coverage for 90.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage
LGBM LGBM 0.149 0.580 0.882
LGBM Logistic Regression 0.114 0.386 0.812
Logistic Regression LGBM 0.151 0.588 0.885
Logistic Regression Logistic Regression 0.112 0.389 0.822

Y(1) - Quantile

Table 5: Coverage for 95.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage
LGBM LGBM 0.059 0.298 0.962
LGBM Logistic Regression 0.054 0.273 0.962
Logistic Regression LGBM 0.059 0.303 0.961
Logistic Regression Logistic Regression 0.057 0.275 0.955
Table 6: Coverage for 90.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage
LGBM LGBM 0.059 0.250 0.913
LGBM Logistic Regression 0.054 0.229 0.910
Logistic Regression LGBM 0.059 0.254 0.919
Logistic Regression Logistic Regression 0.057 0.231 0.898

LQTE

The results are based on a location-scale model as described the corresponding Example with \(10,000\) observations.

The non-uniform results (coverage, ci length and bias) refer to averaged values over all quantiles (point-wise confidende intervals).

DoubleML Version                       0.9.0
Script                       lpq_coverage.py
Date                     2024-09-09 12:37:02
Total Runtime (seconds)         18799.444735
Python Version                        3.12.5
Table 7: Coverage for 95.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage Uniform CI Length Uniform Coverage
LGBM LGBM 0.385 1.950 0.963 2.540 0.970
LGBM Logistic Regression 0.375 1.866 0.949 2.424 0.950
Logistic Regression LGBM 0.372 1.929 0.964 2.487 0.980
Logistic Regression Logistic Regression 0.373 1.864 0.949 2.408 0.950
Table 8: Coverage for 90.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage Uniform CI Length Uniform Coverage
LGBM LGBM 0.385 1.637 0.923 2.255 0.940
LGBM Logistic Regression 0.375 1.566 0.910 2.155 0.900
Logistic Regression LGBM 0.372 1.619 0.919 2.208 0.920
Logistic Regression Logistic Regression 0.373 1.564 0.903 2.136 0.900

Local Potential Quantiles

Local Y(0) - Quantile

Table 9: Coverage for 95.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage
LGBM LGBM 0.232 1.396 0.973
LGBM Logistic Regression 0.228 1.340 0.977
Logistic Regression LGBM 0.221 1.372 0.981
Logistic Regression Logistic Regression 0.207 1.321 0.979
Table 10: Coverage for 90.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage
LGBM LGBM 0.232 1.172 0.940
LGBM Logistic Regression 0.228 1.125 0.950
Logistic Regression LGBM 0.221 1.152 0.948
Logistic Regression Logistic Regression 0.207 1.109 0.953

Local Y(1) - Quantile

Table 11: Coverage for 95.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage
LGBM LGBM 0.328 1.981 0.990
LGBM Logistic Regression 0.322 1.894 0.970
Logistic Regression LGBM 0.301 1.916 0.982
Logistic Regression Logistic Regression 0.306 1.855 0.984
Table 12: Coverage for 90.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage
LGBM LGBM 0.328 1.662 0.958
LGBM Logistic Regression 0.322 1.590 0.940
Logistic Regression LGBM 0.301 1.608 0.960
Logistic Regression Logistic Regression 0.306 1.556 0.947

CVaR Effects

The results are based on a location-scale model as described the corresponding Example with \(5,000\) observations. Remark that the process is not linear.

The non-uniform results (coverage, ci length and bias) refer to averaged values over all quantiles (point-wise confidende intervals).

DoubleML Version                       0.9.0
Script                      cvar_coverage.py
Date                     2024-09-09 11:59:26
Total Runtime (seconds)         16546.961243
Python Version                        3.12.5
Table 13: Coverage for 95.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage Uniform CI Length Uniform Coverage
LGBM LGBM 0.144 0.693 0.949 0.811 0.950
LGBM Logistic Regression 0.123 0.497 0.870 0.583 0.860
Linear LGBM 0.180 0.723 0.865 0.830 0.850
Linear Logistic Regression 0.152 0.541 0.812 0.619 0.800
Table 14: Coverage for 90.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage Uniform CI Length Uniform Coverage
LGBM LGBM 0.144 0.582 0.901 0.706 0.880
LGBM Logistic Regression 0.123 0.417 0.809 0.506 0.780
Linear LGBM 0.180 0.607 0.801 0.718 0.800
Linear Logistic Regression 0.152 0.454 0.709 0.534 0.690

CVaR Potential Quantiles

CVaR Y(0)

Table 15: Coverage for 95.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage
LGBM LGBM 0.139 0.679 0.946
LGBM Logistic Regression 0.119 0.484 0.890
Linear LGBM 0.175 0.691 0.861
Linear Logistic Regression 0.154 0.512 0.778
Table 16: Coverage for 90.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage
LGBM LGBM 0.139 0.570 0.888
LGBM Logistic Regression 0.119 0.406 0.819
Linear LGBM 0.175 0.580 0.770
Linear Logistic Regression 0.154 0.429 0.689

CVaR Y(1)

Table 17: Coverage for 95.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage
LGBM LGBM 0.043 0.227 0.978
LGBM Logistic Regression 0.044 0.212 0.965
Linear LGBM 0.048 0.257 0.976
Linear Logistic Regression 0.049 0.230 0.943
Table 18: Coverage for 90.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage
LGBM LGBM 0.043 0.191 0.932
LGBM Logistic Regression 0.044 0.178 0.915
Linear LGBM 0.048 0.216 0.931
Linear Logistic Regression 0.049 0.193 0.885