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Linear Quantile Regression

Medium · statistical_analysis · Quant Researcher interview question · quantile_regression, linear_programming, tail_risk, robust_regression, statistical_analysis

Quantile regression models the conditional quantiles of a response variable, providing a more comprehensive view of potential outcomes beyond the conditional mean from OLS. In quantitative finance, it is essential for tail-risk analysis, stress testing, and modeling conditional Value-at-Risk (VaR). The estimation is framed as a linear programming problem that minimizes an asymmetric check loss function. Task Implement the function quantile_regression(x: list, y: list, tau: float) to perform a s