Quantile loss and downside estimates
Question
What quantity is estimated by minimising pinball loss at level 0.05, and how would you check the resulting forecasts?
Short answer
Pinball loss targets a conditional fifth percentile, subject to standard existence conditions. Check empirical exceedance frequency and whether exceedances cluster or depend on available predictors. Use chronological evaluation and distinguish return quantiles from positive loss conventions. A correct unconditional 5% exceedance rate alone does not establish conditional calibration or accurate tail-severity estimates.
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Open the worked solutionLessons behind this question
- Ridge, Lasso, and Elastic Net
- The Normal Equations: Closed-Form Least Squares
- Simple Linear Regression: OLS Estimators and Geometry
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