#bandwidth

Question 1: Single choice

hardAI-checkedNearest Neighbors & Kernel Methods

Nadaraya–Watson regression in $d$ dimensions is consistent if its kernel width σ shrinks suitably as the number of points $n$ grows. Which schedule is right?

σ → 0 with $n\sigma^d \to \infty$ ; the best rate, σ ∝ $n^{-1/(d+4)}$ , shrinks more slowly in high $d$ 1
σ → 0 with $n\sigma^d \to \infty$ ; the best rate, σ ∝ $n^{-1/(d+4)}$ , shrinks faster in high $d$ 2
σ stays fixed, since averaging over more points in the same window removes the error3
σ ∝ $1/n$ in every dimension, so that the window narrows as fast as the data arrive4

Timed test