Coarsening Latent-Class Probabilities: Directional Distortion and Coverage Loss
Read the original on arXiv Statistics ML →The paper studies how coarsening a calibrated probability vector—by converting it to a hard label such as an argmax or a confidence threshold—affects the estimation of a treatment effect vector τ in a partially linear regression setting. It shows that the plug‑in estimator converges to a distorted version Δτ, where the distortion operator ΔΔ depends on the regression of the discarded part of the score on the retained part. The authors derive how this distortion drives coverage loss of Wald confidence intervals, provide estimable formulas for the bias and coverage, and demonstrate severe loss in simulations and real‑data audits.
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