Robust Statistics and Bias Correction: Ideas for Differential Privacy and Utility
summary
Argues that using M-estimators with bounded score (Huber family, tuning K between 0.5–2) yields bounded sensitivity so less noise is needed under objective perturbation, and that applying the I‑tilted bootstrap (iterated bootstrap) corrects the finite-sample and asymptotic bias introduced by privatization. Simulations (n = 10, 100, 1,000; ε = 0.1, 1, 2) show the bias‑corrected robust estimator often lowers MSE versus standard truncation-based objective perturbation and competes with the nonprivate mean; requires a parametric generative model and known σ.
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chapters (14)
- 0:00Introduction
- 0:55Connections between Robust Statistics and Differential Privacy
- 2:04M Estimation as Laded
- 3:12Bias Correction
- 4:47What is Robust Statistics
- 5:59Background
- 10:46Sensitivity Curve
- 12:15Influence Function
- 16:15Gross Error Sensitivity
- 18:25M Estimation
- 26:16Bias Correction in Robust Estimation
- 38:21Simulations
- 40:35Comparison
- 45:02Conclusion
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