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Optimal locally private estimation under $\ell_p$ loss for $1\le p\le 2$
In this paper, we sharpen this result by showing asymptotic optimality of the proposed scheme under the $\ell_p^p$ loss for all $1\le p\le 2.$ More precisely, we show that for any $p\in[1, 2]$ and any $k$ and $\epsilon,$ the ratio between the worst-case $\ell_p^p$ estimation loss of our scheme and the optimal value approaches $1$ as the number of samples tends to infinity.
Asymptotically optimal private estimation under mean square loss
In other words, for a large number of samples the worst-case estimation loss of our scheme was shown to differ from the optimal value by at most a constant factor.
Optimal Schemes for Discrete Distribution Estimation under Locally Differential Privacy
For a given $\epsilon,$ we consider the problem of constructing optimal privatization schemes with $\epsilon$-privacy level, i. e., schemes that minimize the expected estimation loss for the worst-case distribution.
