论文信息 - Rate of strong uniform convergence of k-NN density estimates

Rate of strong uniform convergence of k-NN density estimates

Abstract Let f n (x) be the univariate k -nearest neighbor ( k -NN) density estimate proposed by Loftsgaarden and Quesenberry (1965). By using similar techniques as in Bahadur's representation of sample quantiles (1966), and by the recent results on the oscillation of empirical processes by Stute (1982), we derive the rate of strong uniform convergence of f n (x) on some suitably chosen interval J δ . Some comparison with the kernel estimates is given, as well as the choice of the bandwidth sequence relative to the sample size.

Y. Mack | Y. P. Mack

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