Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 223 / 2 / c

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- Solution c

Solution

b ↓ 0

, the Huber estimating equation approaches the sign equation

\sum_{i} sgn (x_{i} - θ) = 0,

whose solution is the sample median. Hence the most B-robust location M-estimator is the median, with minimum gross-error sensitivity

γ^{*} = \frac{1}{2 ϕ ( 0 )} = \frac{π}{2} .

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