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

Hani Samawi, Haresh Rochani, Jing Jing Yin, Daniel F Linder, Robert Vogel

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)1071-1090
Number of pages20
JournalComputational Statistics
Volume33
Issue number2
DOIs
StatePublished - Jun 1 2018

Fingerprint

Kernel Density
Ranked Set Sampling
Sampling Design
Simple Random Sampling
Sampling
Sampling Methods
Probable
Set theory
Asymptotic Properties
Parameter Estimation
Tail
Sample Size
Simulation Study
Kernel density
Parameter estimation
Demonstrate
Random sampling

Keywords

  • Density kernel estimation
  • Duchenne muscular dystrophy
  • Mode estimation
  • Ranked set sampling
  • Simple random sample

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Mathematics

Cite this

Notes on kernel density based mode estimation using more efficient sampling designs. / Samawi, Hani; Rochani, Haresh; Yin, Jing Jing; Linder, Daniel F; Vogel, Robert.

In: Computational Statistics, Vol. 33, No. 2, 01.06.2018, p. 1071-1090.

Research output: Contribution to journalArticle

Samawi, Hani ; Rochani, Haresh ; Yin, Jing Jing ; Linder, Daniel F ; Vogel, Robert. / Notes on kernel density based mode estimation using more efficient sampling designs. In: Computational Statistics. 2018 ; Vol. 33, No. 2. pp. 1071-1090.
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