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Moderate deviations and law of the iterated logarithm in for kernel density estimators

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  • Gao, Fuqing

Abstract

Let fn(x) be the non-parametric kernel density estimator of a density function f(x) based on a kernel function K. In this paper, we first prove two moderate deviation theorems in for {fn(x),n>=1}. Then, as an application of the moderate deviations, we obtain a law of the iterated logarithm for {||fn-Efn||1,n>=1}.

Suggested Citation

  • Gao, Fuqing, 2008. "Moderate deviations and law of the iterated logarithm in for kernel density estimators," Stochastic Processes and their Applications, Elsevier, vol. 118(3), pages 452-473, March.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:3:p:452-473
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    References listed on IDEAS

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    1. Djamal Louani, 1998. "Large Deviations Limit Theorems for the Kernel Density Estimator," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 243-253, March.
    2. Lei, Liangzhen & Wu, Liming, 2005. "Large deviations of kernel density estimator in L1(Rd) for uniformly ergodic Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 115(2), pages 275-298, February.
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    Cited by:

    1. Lulu Fang & Min Wu & Lei Shang, 2018. "Large and Moderate Deviation Principles for Engel Continued Fractions," Journal of Theoretical Probability, Springer, vol. 31(1), pages 294-318, March.

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