Quantile Models

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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                       0.8.2
Script                        pq_coverage.py
Date                     2024-08-14 14:35:29
Total Runtime (seconds)         13704.297192
Python Version                        3.12.4
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 0.123 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 0.914 0.720 0.860
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 1.031 0.920
LGBM Logistic Regression 0.123 0.426 0.829 0.715 0.840
Logistic Regression LGBM 0.159 0.629 0.894 1.034 0.920
Logistic Regression Logistic Regression 0.124 0.434 0.844 0.719 0.850

Potential Quantiles

Y(0) - Quantile

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 0.904
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 0.813
Logistic Regression LGBM 0.151 0.588 0.886
Logistic Regression Logistic Regression 0.112 0.389 0.825

Y(1) - Quantile

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 0.954
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 0.911
Logistic Regression LGBM 0.059 0.254 0.920
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                       0.8.2
Script                       lpq_coverage.py
Date                     2024-08-14 19:43:50
Total Runtime (seconds)         18405.714146
Python Version                        3.12.4
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 1.951 0.963 2.541 0.970
LGBM Logistic Regression 0.375 1.868 0.950 2.427 0.960
Logistic Regression LGBM 0.372 1.929 0.964 2.488 0.980
Logistic Regression Logistic Regression 0.372 1.865 0.950 2.411 0.950
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 0.922 2.537 0.970
LGBM Logistic Regression 0.375 1.568 0.908 2.430 0.960
Logistic Regression LGBM 0.372 1.619 0.919 2.491 0.970
Logistic Regression Logistic Regression 0.372 1.565 0.906 2.410 0.950

Local Potential Quantiles

Local Y(0) - Quantile

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 0.227 1.341 0.977
Logistic Regression LGBM 0.221 1.372 0.981
Logistic Regression Logistic Regression 0.206 1.321 0.978
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 1.126 0.950
Logistic Regression LGBM 0.221 1.152 0.950
Logistic Regression Logistic Regression 0.206 1.109 0.953

Local Y(1) - Quantile

Coverage for 95.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage
LGBM LGBM 0.328 1.982 0.990
LGBM Logistic Regression 0.322 1.896 0.970
Logistic Regression LGBM 0.301 1.916 0.982
Logistic Regression Logistic Regression 0.306 1.856 0.984
Coverage for 90.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage
LGBM LGBM 0.328 1.663 0.956
LGBM Logistic Regression 0.322 1.591 0.940
Logistic Regression LGBM 0.301 1.608 0.960
Logistic Regression Logistic Regression 0.306 1.558 0.946

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                       0.8.2
Script                      cvar_coverage.py
Date                     2024-08-14 10:41:51
Total Runtime (seconds)         13995.808331
Python Version                        3.12.4
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 0.873 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
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 0.903 0.814 0.970
LGBM Logistic Regression 0.123 0.417 0.810 0.582 0.860
Linear LGBM 0.179 0.607 0.802 0.831 0.860
Linear Logistic Regression 0.152 0.454 0.712 0.617 0.790

CVaR Potential Quantiles

CVaR Y(0)

Coverage for 95.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage
LGBM LGBM 0.139 0.679 0.945
LGBM Logistic Regression 0.119 0.484 0.891
Linear LGBM 0.175 0.691 0.859
Linear Logistic Regression 0.155 0.512 0.777
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 0.816
Linear LGBM 0.175 0.580 0.769
Linear Logistic Regression 0.155 0.429 0.688

CVaR Y(1)

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 0.964
Linear LGBM 0.047 0.257 0.978
Linear Logistic Regression 0.049 0.230 0.941
Coverage for 90.0%-Confidence Interval over 100 Repetitions
Learner g Learner m Bias CI Length Coverage
LGBM LGBM 0.044 0.191 0.931
LGBM Logistic Regression 0.044 0.178 0.912
Linear LGBM 0.047 0.216 0.931
Linear Logistic Regression 0.049 0.193 0.882