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                         0.12.dev0
Script                        PQCoverageSimulation
Date                              2025-12-04 19:07
Total Runtime (minutes)                 117.313274
Python Version                              3.12.3
Config File              scripts/irm/pq_config.yml
ⓘLearner g Learner m Bias CI Length Coverage Uniform CI Length Uniform Coverage
LGBM Clas. LGBM Clas. 0.156 0.735 0.934 0.982 0.880
LGBM Clas. Logistic 0.128 0.538 0.924 0.720 0.865
Logistic LGBM Clas. 0.146 0.727 0.950 0.962 0.935
Logistic Logistic 0.120 0.539 0.936 0.716 0.915
Coverage for 95%-Confidence Interval over 200 Repetitions
ⓘLearner g Learner m Bias CI Length Coverage Uniform CI Length Uniform Coverage
LGBM Clas. LGBM Clas. 0.156 0.617 0.882 0.884 0.815
LGBM Clas. Logistic 0.128 0.452 0.848 0.647 0.800
Logistic LGBM Clas. 0.146 0.610 0.899 0.861 0.865
Logistic Logistic 0.120 0.453 0.871 0.641 0.850
Coverage for 90%-Confidence Interval over 200 Repetitions

Potential Quantiles

Y(0) - Quantile

ⓘLearner g Learner m Bias CI Length Coverage
LGBM Clas. LGBM Clas. 0.143 0.688 0.939
LGBM Clas. Logistic 0.115 0.487 0.914
Logistic LGBM Clas. 0.133 0.676 0.953
Logistic Logistic 0.103 0.483 0.945
Coverage for 95%-Confidence Interval over 200 Repetitions
ⓘLearner g Learner m Bias CI Length Coverage
LGBM Clas. LGBM Clas. 0.143 0.577 0.884
LGBM Clas. Logistic 0.115 0.409 0.861
Logistic LGBM Clas. 0.133 0.567 0.904
Logistic Logistic 0.103 0.405 0.894
Coverage for 90%-Confidence Interval over 200 Repetitions

Y(1) - Quantile

ⓘLearner g Learner m Bias CI Length Coverage
LGBM Clas. LGBM Clas. 0.062 0.303 0.955
LGBM Clas. Logistic 0.057 0.283 0.948
Logistic LGBM Clas. 0.061 0.302 0.953
Logistic Logistic 0.056 0.283 0.949
Coverage for 95%-Confidence Interval over 200 Repetitions
ⓘLearner g Learner m Bias CI Length Coverage
LGBM Clas. LGBM Clas. 0.062 0.255 0.899
LGBM Clas. Logistic 0.057 0.237 0.900
Logistic LGBM Clas. 0.061 0.254 0.910
Logistic Logistic 0.056 0.237 0.909
Coverage for 90%-Confidence Interval over 200 Repetitions

LQTE

The results are based on a location-scale model as described the corresponding Example with \(5,000\) observations.

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

DoubleML Version                          0.12.dev0
Script                        LPQCoverageSimulation
Date                               2025-12-04 19:04
Total Runtime (minutes)                  114.709041
Python Version                               3.12.3
Config File              scripts/irm/lpq_config.yml
ⓘLearner g Learner m Bias CI Length Coverage Uniform CI Length Uniform Coverage
LGBM Clas. LGBM Clas. 0.386 1.962 0.950 2.454 0.940
LGBM Clas. Logistic 0.364 1.891 0.946 2.367 0.940
Logistic LGBM Clas. 0.364 1.910 0.951 2.386 0.955
Logistic Logistic 0.361 1.844 0.942 2.300 0.950
Coverage for 95%-Confidence Interval over 200 Repetitions
ⓘLearner g Learner m Bias CI Length Coverage Uniform CI Length Uniform Coverage
LGBM Clas. LGBM Clas. 0.386 1.646 0.905 2.172 0.905
LGBM Clas. Logistic 0.364 1.587 0.889 2.092 0.905
Logistic LGBM Clas. 0.364 1.603 0.895 2.108 0.905
Logistic Logistic 0.361 1.548 0.890 2.029 0.890
Coverage for 90%-Confidence Interval over 200 Repetitions

Local Potential Quantiles

Local Y(0) - Quantile

ⓘLearner g Learner m Bias CI Length Coverage
LGBM Clas. LGBM Clas. 0.237 1.420 0.965
LGBM Clas. Logistic 0.227 1.368 0.969
Logistic LGBM Clas. 0.222 1.387 0.970
Logistic Logistic 0.219 1.332 0.973
Coverage for 95%-Confidence Interval over 200 Repetitions
ⓘLearner g Learner m Bias CI Length Coverage
LGBM Clas. LGBM Clas. 0.237 1.192 0.933
LGBM Clas. Logistic 0.227 1.148 0.935
Logistic LGBM Clas. 0.222 1.164 0.937
Logistic Logistic 0.219 1.118 0.939
Coverage for 90%-Confidence Interval over 200 Repetitions

Local Y(1) - Quantile

ⓘLearner g Learner m Bias CI Length Coverage
LGBM Clas. LGBM Clas. 0.325 1.981 0.973
LGBM Clas. Logistic 0.297 1.909 0.973
Logistic LGBM Clas. 0.309 1.916 0.969
Logistic Logistic 0.296 1.854 0.973
Coverage for 95%-Confidence Interval over 200 Repetitions
ⓘLearner g Learner m Bias CI Length Coverage
LGBM Clas. LGBM Clas. 0.325 1.663 0.938
LGBM Clas. Logistic 0.297 1.602 0.939
Logistic LGBM Clas. 0.309 1.608 0.941
Logistic Logistic 0.296 1.556 0.935
Coverage for 90%-Confidence Interval over 200 Repetitions

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                           0.12.dev0
Script                        CVARCoverageSimulation
Date                                2025-12-04 18:37
Total Runtime (minutes)                    87.475292
Python Version                                3.12.3
Config File              scripts/irm/cvar_config.yml
ⓘLearner g Learner m Bias CI Length Coverage Uniform CI Length Uniform Coverage
LGBM Regr. LGBM Clas. 0.161 0.680 0.889 0.795 0.895
LGBM Regr. Logistic 0.124 0.524 0.889 0.615 0.870
Linear LGBM Clas. 0.184 0.702 0.862 0.807 0.840
Linear Logistic 0.153 0.566 0.834 0.648 0.800
Coverage for 95%-Confidence Interval over 200 Repetitions
ⓘLearner g Learner m Bias CI Length Coverage Uniform CI Length Uniform Coverage
LGBM Regr. LGBM Clas. 0.161 0.571 0.828 0.691 0.785
LGBM Regr. Logistic 0.124 0.440 0.827 0.533 0.815
Linear LGBM Clas. 0.184 0.589 0.789 0.698 0.745
Linear Logistic 0.153 0.475 0.771 0.560 0.735
Coverage for 90%-Confidence Interval over 200 Repetitions

CVaR Potential Quantiles

CVaR Y(0)

ⓘLearner g Learner m Bias CI Length Coverage
LGBM Regr. LGBM Clas. 0.161 0.666 0.877
LGBM Regr. Logistic 0.128 0.511 0.877
Linear LGBM Clas. 0.175 0.671 0.849
Linear Logistic 0.148 0.536 0.835
Coverage for 95%-Confidence Interval over 200 Repetitions
ⓘLearner g Learner m Bias CI Length Coverage
LGBM Regr. LGBM Clas. 0.161 0.559 0.814
LGBM Regr. Logistic 0.128 0.428 0.830
Linear LGBM Clas. 0.175 0.563 0.789
Linear Logistic 0.148 0.450 0.742
Coverage for 90%-Confidence Interval over 200 Repetitions

CVaR Y(1)

ⓘLearner g Learner m Bias CI Length Coverage
LGBM Regr. LGBM Clas. 0.041 0.228 0.966
LGBM Regr. Logistic 0.039 0.215 0.966
Linear LGBM Clas. 0.042 0.254 0.976
Linear Logistic 0.042 0.234 0.974
Coverage for 95%-Confidence Interval over 200 Repetitions
ⓘLearner g Learner m Bias CI Length Coverage
LGBM Regr. LGBM Clas. 0.041 0.192 0.931
LGBM Regr. Logistic 0.039 0.181 0.931
Linear LGBM Clas. 0.042 0.213 0.951
Linear Logistic 0.042 0.197 0.929
Coverage for 90%-Confidence Interval over 200 Repetitions