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Uniform strong consistency of kernel density estimators under dependence. (English) Zbl 0843.62041
Summary: It is shown that the kernel density estimators converge a.s. uniformly on compact subsets of the variable under $\alpha$-mixing. In particular, the rates of convergence for the estimators will be investigated to analyze dependency effects.

62G07Density estimation
62G20Nonparametric asymptotic efficiency
Full Text: DOI
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[2] Cox; D.; Kim, T. Y.: Moment bounds for mixing random variables useful in nonparametric function estimation. Stochastic process appl. 56, 151-158 (1995) · Zbl 0817.62027
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