Rate of strong uniform convergence of k-NN density estimates
The author uses recent results of \textit{W. Stute} [Ann. Probab. 10, 86-107 and 414-422 (1982; Zbl 0489.60038 and Zbl 0493.62040, respectively)] on the oscillation behavior of empirical processes to derive the rate of strong uniform convergence of the kth-nearest neighbor density estimator \(f_ n(x)\) to the true density f(x) on a closed interval J on which f is uniformly bounded above and below. Here \(f_ n(\cdot)\) is based on a sample of size n from density f, \(k=k(n)\) grows with n at a controlled rate, and some differentiability conditions are imposed on f.
scientific article; zbMATH DE number 3852218
scientific article