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On empirical estimation of mode based on weakly dependent samples

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  • Liu, Bowen
  • Ghosh, Sujit K.

Abstract

Given a large sample of observations from an unknown univariate continuous distribution, it is often of interest to empirically estimate the global mode of the underlying density. Applications include samples obtained by Monte Carlo methods with independent observations, or Markov Chain Monte Carlo methods with weakly dependent samples from the underlying stationary density. In either case, often the generating density is not available in closed form and only empirical determination of the mode is possible. Assuming that the generating density has a unique global mode, a non-parametric estimate of the density is proposed based on a sequence of mixtures of Beta densities which allows for the estimation of the mode even when the mode is possibly located on the boundary of the support of the density. Furthermore, the estimated mode is shown to be strongly universally consistent under a set of mild regularity conditions. The proposed method is compared with other empirical estimates of the mode based on popular kernel density estimates. Numerical results based on extensive simulation studies show benefits of the proposed methods in terms of empirical bias, standard errors and computation time. An R package implementing the method is also made available online.

Suggested Citation

  • Liu, Bowen & Ghosh, Sujit K., 2020. "On empirical estimation of mode based on weakly dependent samples," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:csdana:v:152:y:2020:i:c:s0167947320301377
    DOI: 10.1016/j.csda.2020.107046
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    References listed on IDEAS

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    1. Turnbull, Bradley C. & Ghosh, Sujit K., 2014. "Unimodal density estimation using Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 13-29.
    2. Babu, G. Jogesh & Chaubey, Yogendra P., 2006. "Smooth estimation of a distribution and density function on a hypercube using Bernstein polynomials for dependent random vectors," Statistics & Probability Letters, Elsevier, vol. 76(9), pages 959-969, May.
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    Cited by:

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    2. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).

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