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Uniform convergence rates for a nearest neighbor density estimator under dependence assumptions. (English) Zbl 0899.62066

Summary: The rates of strong uniform convergence over any compact set for an alternative nearest neighbor density estimator are obtained when the observations satisfy a \(\phi\)-mixing or an \(\alpha\)-mixing condition. In the \(\phi\)-mixing case we obtain a quite better convergence rate than for \(\alpha\)-mixing processes and we do not require a geometric condition on the mixing coefficients. For independent or \(m\)-dependent observations, as a special case of \(\phi\)-mixing, the result gives us the optimal rate of strong uniform convergence for density estimators.

MSC:

62G20 Asymptotic properties of nonparametric inference
62G07 Density estimation
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