Modelling the extreme using Quantile Regression
summary
Shows how conditional quantiles are estimated directly using linear econometric models and non‑linear methods implemented in tensorflow or xgboost, optimizing the pinball loss to target a specific alpha such as the 90th percentile. Demonstrates linear statsmodels fits, neural nets that output multiple quantiles at once, and applications where neural quantile models beat baselines on electricity demand benchmarks. Notes practical issues: balancing multi‑quantile outputs, checking empirical coverage (expect underprediction ≈1−alpha), and evaluating with pinball and Winkler scores.
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chapters (9)
- 0:00Quantile Regression intro
- 1:30Why Quantile Regression matters
- 4:20Naive to conditional quantiles
- 8:57Mathematical formulation
- 13:59Quantile vs OLS
- 19:44Median estimation proof
- 21:11Implementing Quantile Regression
- 24:21Evaluating models
- 25:46Key takeaways
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