Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 223 / 3 / e

Table of contents
- Solution e

Solution

The test statistic is generated by the functional

T (F) = \int q_{c} (x) d F (x)

. At

F = P_{0}

, its influence function is

IF_{t es t} (x; T, P_{0}) = q_{c} (x) - E_{P_{0}} [q_{c} (X)] .

Because

∣ q_{c} (x) ∣ \leq c

, this influence function is bounded. Multiplying

q_{c}

by the constant inherited from the clipped log-likelihood ratio only rescales the same bounded expression.

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