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A note on the convergence rate of the kernel density estimator of the mode

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  • Shi, Xiaoping
  • Wu, Yuehua
  • Miao, Baiqi

Abstract

In this paper, the mode estimator based on the Parzen-Rosenblatt kernel estimator is considered [Parzen, E., 1962. On estimating probability density function and mode. The Annals of Mathematical Statistics 33, 1065-1076]. In light of Shi et al. [Shi, X., Wu, Y., Miao, B., 2009. Strong convergence rate of estimators of change point and its application. Computational Statistics & Data Analysis 53, 990-998], under mild conditions, we establish the relationship between the convergence rate of the mode estimator and the window width. In this way, we obtain a better convergence rate of the mode estimator.

Suggested Citation

  • Shi, Xiaoping & Wu, Yuehua & Miao, Baiqi, 2009. "A note on the convergence rate of the kernel density estimator of the mode," Statistics & Probability Letters, Elsevier, vol. 79(17), pages 1866-1871, September.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:17:p:1866-1871
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    References listed on IDEAS

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    1. Kokoszka, Piotr & Leipus, Remigijus, 1998. "Change-point in the mean of dependent observations," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 385-393, November.
    2. Frédéric Ferraty & Ali Laksaci & Philippe Vieu, 2006. "Estimating Some Characteristics of the Conditional Distribution in Nonparametric Functional Models," Statistical Inference for Stochastic Processes, Springer, vol. 9(1), pages 47-76, May.
    3. Vieu, Philippe, 1996. "A note on density mode estimation," Statistics & Probability Letters, Elsevier, vol. 26(4), pages 297-307, March.
    4. Shi, Xiaoping & Wu, Yuehua & Miao, Baiqi, 2009. "Strong convergence rate of estimators of change point and its application," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 990-998, February.
    5. Herrmann, Eva & Ziegler, Klaus, 2004. "Rates of consistency for nonparametric estimation of the mode in absence of smoothness assumptions," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 359-368, July.
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    Cited by:

    1. Li Zhaoyuan & Tian Maozai, 2017. "Detecting Change-Point via Saddlepoint Approximations," Journal of Systems Science and Information, De Gruyter, vol. 5(1), pages 48-73, February.
    2. Eunju Hwang & Dong Shin, 2016. "Kernel estimators of mode under $$\psi $$ ψ -weak dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 301-327, April.

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