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Consistency of kernel density estimators for causal processes

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Abstract

Using the blocking techniques and m-dependent methods, the asymptotic behavior of kernel density estimators for a class of stationary processes, which includes some nonlinear time series models, is investigated. First, the pointwise and uniformly weak convergence rates of the deviation of kernel density estimator with respect to its mean (and the true density function) are derived. Secondly, the corresponding strong convergence rates are investigated. It is showed, under mild conditions on the kernel functions and bandwidths, that the optimal rates for the i.i.d. density models are also optimal for these processes.

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  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    ZhengYan Lin & YueXu Zhao

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  1. ZhengYan Lin
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  2. YueXu Zhao
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Correspondence to YueXu Zhao.

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Lin, Z., Zhao, Y. Consistency of kernel density estimators for causal processes. Sci. China Math. 57, 1083–1108 (2014). https://doi.org/10.1007/s11425-014-4774-6

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