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A note on density mode estimation

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  • Vieu, Philippe

Abstract

Four nonparametric estimates of the mode of a density function are investigated. Two mode estimates are defined from a global (resp. from a local) kernel density estimate, while the other two are defined from a global (resp. from a local) kernel estimate of the first derivative of the density function. We show that each of these mode estimates attains the same rate of convergence as the usual sample model (Eddy, 1980). Then, Monte-Carlo simulations illustrate on finite samples the utility of the method based on the local estimate of the first derivative.

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  • Vieu, Philippe, 1996. "A note on density mode estimation," Statistics & Probability Letters, Elsevier, vol. 26(4), pages 297-307, March.
    • Handle: RePEc:eee:stapro:v:26:y:1996:i:4:p:297-307
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    1. Marron, J S, 1988. "Automatic Smoothing Parameter Selection: A Survey," Empirical Economics, Springer, vol. 13(3/4), pages 187-208.
    2. Hall, Peter & Schucany, William R., 1989. "A local cross-validation algorithm," Statistics & Probability Letters, Elsevier, vol. 8(2), pages 109-117, June.
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    Cited by:

    1. Ouafae Benrabah & Elias Ould Saïd & Abdelkader Tatachak, 2015. "A kernel mode estimate under random left truncation and time series model: asymptotic normality," Statistical Papers, Springer, vol. 56(3), pages 887-910, August.
    2. Leclerc J., 2000. "Strong Limiting Behavior Of Two Estimates Of The Mode : The Shorth And The Naive Estimator," Statistics & Risk Modeling, De Gruyter, vol. 18(4), pages 413-428, April.
    3. Han-Ying Liang & Jacobo Uña-Álvarez, 2010. "Asymptotic normality for estimator of conditional mode under left-truncated and dependent observations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(1), pages 1-19, July.
    4. Hsu, Chih-Yuan & Wu, Tiee-Jian, 2013. "Efficient estimation of the mode of continuous multivariate data," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 148-159.
    5. 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.
    6. Barbara Wieczorek, 2010. "On optimal estimation of the mode in nonparametric deconvolution problems," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(1), pages 65-80.
    7. José E. Chacón, 2020. "The Modal Age of Statistics," International Statistical Review, International Statistical Institute, vol. 88(1), pages 122-141, April.
    8. 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.
    9. 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.
    10. A. Quintela-Del-Río & Ph. Vieu, 1997. "A nonparametric conditional mode estimate," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 8(3), pages 253-266, September.
    11. Obereder, Andreas & Scherzer, Otmar & Kovac, Arne, 2007. "Bivariate density estimation using BV regularisation," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5622-5634, August.
    12. Rachdi, Mustapha & Sabre, Rachid, 2000. "Consistent estimates of the mode of the probability density function in nonparametric deconvolution problems," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 105-114, April.
    13. Horová Ivana & Vieu Philippe & Zelinka Jiří, 2002. "Optimal Choice Of Nonparametric Estimates Of A Density And Of Its Derivatives," Statistics & Risk Modeling, De Gruyter, vol. 20(1-4), pages 355-378, April.
    14. Kunhui Zhang & Yen-Chi Chen, 2021. "Refined Mode-Clustering via the Gradient of Slope," Stats, MDPI, vol. 4(2), pages 1-23, June.

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