# 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 0.8.2
Script pq_coverage.py
Date 2024-08-14 14:35:29
Total Runtime (seconds) 13704.297192
Python Version 3.12.4
```

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 |

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

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 |

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

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 |

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
```

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 |

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

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 |

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

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 |

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
```

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 |

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)

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 |

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)

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 |

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 |