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Notes on kernel density based mode estimation using more efficient sampling designs

Author

Listed:
  • Hani Samawi

    (Georgia Southern University)

  • Haresh Rochani

    (Georgia Southern University)

  • JingJing Yin

    (Georgia Southern University)

  • Daniel Linder

    (Augusta University)

  • Robert Vogel

    (Georgia Southern University)

Abstract

The mode is a measure of the central tendency as well as the most probable value. Additionally, the mode is not influenced by the tail of the distribution. In the literature the properties and the application of mode estimation is only considered under simple random sampling (SRS). However, ranked set sampling (RSS) is a structural sampling method which improves the efficiency of parameter estimation in many circumstances and typically leads to a reduction in sample size. In this paper we investigate some of the asymptotic properties of kernel density based mode estimation using RSS. We demonstrate that kernel density based mode estimation using RSS is consistent and asymptotically normal with smaller variance than that under SRS. Improved performance of the mode estimation using RSS compared to SRS is supported through a simulation study. An illustration of the computational aspect using a Duchenne muscular dystrophy data set is provided.

Suggested Citation

  • Hani Samawi & Haresh Rochani & JingJing Yin & Daniel Linder & Robert Vogel, 2018. "Notes on kernel density based mode estimation using more efficient sampling designs," Computational Statistics, Springer, vol. 33(2), pages 1071-1090, June.
    • Handle: RePEc:spr:compst:v:33:y:2018:i:2:d:10.1007_s00180-017-0787-2
    DOI: 10.1007/s00180-017-0787-2
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    References listed on IDEAS

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    1. DiNardo, John & Fortin, Nicole M & Lemieux, Thomas, 1996. "Labor Market Institutions and the Distribution of Wages, 1973-1992: A Semiparametric Approach," Econometrica, Econometric Society, vol. 64(5), pages 1001-1044, September.
    2. Haiying Chen & Elizabeth A. Stasny & Douglas A. Wolfe, 2006. "Unbalanced Ranked Set Sampling for Estimating a Population Proportion," Biometrics, The International Biometric Society, vol. 62(1), pages 150-158, March.
    3. Emili Tortosa-Ausina, 2002. "Financial costs, operating costs, and specialization of Spanish banking firms as distribution dynamics," Applied Economics, Taylor & Francis Journals, vol. 34(17), pages 2165-2176.
    4. Johan Lim & Min Chen & Sangun Park & Xinlei Wang & Lynne Stokes, 2014. "Kernel Density Estimator From Ranked Set Samples," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(10-12), pages 2156-2168, May.
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