Large Sample Properties of Nearest Neighbor Density Function Estimators

摘要: Publisher Summary This chapter presents the assumption that Let X1, X2,… are iid random variables having unknown density function f with respect to Lebesgue measure λ on Euclidean p-space RP. It an estimation of f(z) for a given z. A nearest neighbor estimator is gn(z) = k(n)/n/λ{S(R(n))}. simply empiric divided by region S(R(n)). essentially due Fix and Hodges, was explicitly introduced studied Loftsgaarden Quesenberry. These subsequent authors used norm, but p > 1, other norms may be useful proofs unaffected this generality.