For mean estimation, a simple thresholding operator on privacy budgets matches the performance of fully personalized differential privacy mechanisms up to constant factors.
Optimal and differentially private data acquisition: Central and local mechanisms.Operations Research, 72(3):1105–1123
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Limits of Personalizing Differential Privacy Budgets
For mean estimation, a simple thresholding operator on privacy budgets matches the performance of fully personalized differential privacy mechanisms up to constant factors.