Identification and Inference with Min-over-max Estimators for the Measurement of Labor Market Fairness
劳动市场公平性度量中最小—最大估计量的识别与推断
These notes shows how to do inference on the Demographic Parity (DP) metric. Although the metric is a complex statistic involving min and max computations, we propose a smooth approximation of those functions and derive its asymptotic distribution. The limit of these approximations and their gradients converge to those of the true max and min functions, wherever they exist. More importantly, when the true max and min functions are not differentiable, the approximations still…