Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 218 / 3 / b / Solution

The $L$-nearest-neighbour classifier finds the $L$ training predictors nearest to $x$ and returns the majority class among their labels. Increasing $L$ averages more labels and reduces variance of an estimator, but uses observations farther from $x$ and therefore increases bias of an estimator; decreasing $L$ reverses this bias-variance tradeoff.