How do you choose the KDE bandwidth?

hard

Answer

$(1) Silverman's rule: h = (4/(d+2))^(1/(d+4)) * σ * n^(-1/(d+4)) — closed form, assumes Gaussian data.$
$(2) Scott's rule: similar but different exponent.$
$(3) Cross-validation of log-likelihood \to most principled, more expensive.$
$(4) Adaptive bandwidth: h varies with local density.$
$Small h \to overfit / spiky; large h \to over-smooth.$
$Rule: start with Silverman, refine with CV if it matters.$

Check yourself — multiple choice

Random
Silverman / Scott closed forms (assume Gaussian) or CV on log-lik (best); small h = spiky, large h = over-smooth; adaptive bandwidth for local variation
Same as k
Not real

KDE bandwidth: Silverman / Scott / CV of log-lik; small = spiky, large = over-smooth.

#density

214 interview questions in this topic.