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On Consistency in Nonparametric Estimation under Mixing Conditions


  • Irle, A.


In this paper a method for obtaining a.s. consistency in nonparametric estimation is presented which only requires the handling of covariances. This method is applied to kernel density estimation and kernel and nearest neighbour regression estimation. It leads to conditions for a.s. consistency which relax known conditions and include long-range dependence.

Suggested Citation

  • Irle, A., 1997. "On Consistency in Nonparametric Estimation under Mixing Conditions," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 123-147, January.
  • Handle: RePEc:eee:jmvana:v:60:y:1997:i:1:p:123-147

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    Cited by:

    1. Walk, Harro, 2010. "Strong consistency of kernel estimates of regression function under dependence," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1147-1156, August.
    2. Sören Christensen & Albrecht Irle & Lars Willert, 2016. "Classification error in multiclass discrimination from Markov data," Statistical Inference for Stochastic Processes, Springer, vol. 19(3), pages 321-336, October.
    3. Steinwart, Ingo & Hush, Don & Scovel, Clint, 2009. "Learning from dependent observations," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 175-194, January.
    4. Otneim, Håkon & Tjøstheim, Dag, 2016. "Non-parametric estimation of conditional densities: A new method," Discussion Papers 2016/22, Norwegian School of Economics, Department of Business and Management Science.
    5. Zudi Lu, 2001. "Asymptotic Normality of Kernel Density Estimators under Dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 447-468, September.


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