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                   0.10.dev0
Script                        pq_coverage.py
Date                     2025-01-08 17:13:20
Total Runtime (seconds)         17871.711226
Python Version                        3.12.8
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 0.940 1.031 0.910
LGBM Logistic Regression 0.123 0.507 0.909 0.714 0.840
Logistic Regression LGBM 0.159 0.749 0.947 1.029 0.920
Logistic Regression Logistic Regression 0.124 0.518 0.912 0.720 0.850
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 0.123 0.426 0.827 0.646 0.780
Logistic Regression LGBM 0.159 0.629 0.897 0.931 0.870
Logistic Regression Logistic Regression 0.124 0.434 0.841 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 0.888
Logistic Regression LGBM 0.151 0.701 0.942
Logistic Regression Logistic Regression 0.112 0.464 0.905
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 0.884
LGBM Logistic Regression 0.114 0.386 0.812
Logistic Regression LGBM 0.151 0.588 0.886
Logistic Regression Logistic Regression 0.112 0.390 0.825

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 0.961
LGBM Logistic Regression 0.054 0.273 0.962
Logistic Regression LGBM 0.059 0.303 0.962
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 0.914
LGBM Logistic Regression 0.054 0.229 0.913
Logistic Regression LGBM 0.059 0.254 0.917
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                   0.10.dev0
Script                       lpq_coverage.py
Date                     2025-01-08 17:24:33
Total Runtime (seconds)         18545.282371
Python Version                        3.12.8
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 1.868 0.950 2.427 0.950
Logistic Regression LGBM 0.372 1.929 0.964 2.487 0.980
Logistic Regression Logistic Regression 0.372 1.864 0.948 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 1.568 0.908 2.157 0.910
Logistic Regression LGBM 0.372 1.619 0.919 2.208 0.920
Logistic Regression Logistic Regression 0.372 1.564 0.908 2.137 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 0.972
LGBM Logistic Regression 0.227 1.340 0.976
Logistic Regression LGBM 0.221 1.372 0.981
Logistic Regression Logistic Regression 0.206 1.322 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 0.227 1.125 0.950
Logistic Regression LGBM 0.221 1.152 0.950
Logistic Regression Logistic Regression 0.206 1.110 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 1.896 0.970
Logistic Regression LGBM 0.301 1.916 0.982
Logistic Regression Logistic Regression 0.305 1.854 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 1.591 0.941
Logistic Regression LGBM 0.301 1.608 0.960
Logistic Regression Logistic Regression 0.305 1.556 0.948

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                   0.10.dev0
Script                      cvar_coverage.py
Date                     2025-01-08 16:49:01
Total Runtime (seconds)         16412.116838
Python Version                        3.12.8
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 0.940
LGBM Logistic Regression 0.123 0.497 0.874 0.584 0.860
Linear LGBM 0.179 0.723 0.865 0.830 0.850
Linear Logistic Regression 0.152 0.541 0.815 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 0.904 0.706 0.880
LGBM Logistic Regression 0.123 0.417 0.810 0.506 0.780
Linear LGBM 0.179 0.607 0.802 0.718 0.800
Linear Logistic Regression 0.152 0.454 0.713 0.534 0.710

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 0.118 0.484 0.889
Linear LGBM 0.175 0.691 0.862
Linear Logistic Regression 0.155 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 0.118 0.406 0.819
Linear LGBM 0.175 0.580 0.769
Linear Logistic Regression 0.155 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 0.044 0.227 0.978
LGBM Logistic Regression 0.044 0.212 0.963
Linear LGBM 0.047 0.257 0.977
Linear Logistic Regression 0.049 0.230 0.942
Table 18: Coverage for 90.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage
LGBM LGBM 0.044 0.191 0.932
LGBM Logistic Regression 0.044 0.178 0.913
Linear LGBM 0.047 0.216 0.929
Linear Logistic Regression 0.049 0.193 0.882