Order the observations so that
$$
\lVert X_{(1)}-x\rVert_\infty\leq\cdots\leq
\lVert X_{(n)}-x\rVert_\infty,
$$
using a fixed or randomized rule for ties. The <L-nearest-neighbour classifier> estimates
$$
\widehat p_k(x)=\frac1L\sum_{\ell=1}^L
\mathbf1_{\{Y_{(\ell)}=k\}},
\qquad k=1,2,
$$
and predicts a class maximizing $\widehat p_k(x)$.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 218 / 2 / a / Solution

{c}
{title2=$L$-NN}
{wiki=K-nearest_neighbors_algorithm}

The L-nearest-neighbour classifier estimates each class probability by its empirical frequency among the $L$ nearest training covariates and predicts a class of greatest estimated probability.


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 Incoming links: L-nearest-neighbour classifier