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A new quantile estimator with weights based on a subsampling approach.

Gözde Navruz1, A Fırat Özdemir1

  • 1Department of Statistics, Faculty of Sciences, Dokuz Eylül University, İzmir, Turkey.

The British Journal of Mathematical and Statistical Psychology
|January 17, 2020
PubMed
Summary

A novel quantile estimator, NO, improves accuracy for lower and upper quantiles, especially with small samples. This new statistical method also enhances Type I error control in group comparisons.

Keywords:
NO quantile estimatorasymptotic propertiespercentile bootstraptwo independent groups

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Area of Science:

  • Statistics
  • Statistical Modeling
  • Data Analysis

Background:

  • Quantiles are essential in statistics for data analysis and interpretation.
  • Accurate quantile estimation is crucial, particularly for extreme values and small datasets.
  • Existing estimators may lack efficiency or robustness in specific scenarios.

Purpose of the Study:

  • Introduce a new quantile estimator, termed NO.
  • Evaluate the performance and properties of the NO estimator.
  • Compare the NO estimator against established methods like Harrell-Davis, R default, SV2, and kernel estimators.

Main Methods:

  • Developed a novel quantile estimator (NO) as a weighted average of order statistics.
  • Assessed asymptotic properties of the NO estimator.
  • Conducted comparative efficiency analyses against four other quantile estimators.
  • Applied the NO estimator in a percentile bootstrap method for comparing two independent groups.

Main Results:

  • The NO estimator demonstrates desirable asymptotic properties.
  • NO exhibited superior efficiency compared to Harrell-Davis, R default, SV2, and kernel estimators in most experimental settings.
  • When used for comparing two independent groups via percentile bootstrap, NO effectively controlled Type I error rates, outperforming other estimators.

Conclusions:

  • The NO quantile estimator offers improved performance, especially for lower and upper quantiles with small sample sizes.
  • NO provides practical advantages in efficiency and statistical accuracy over existing methods.
  • The NO estimator is a valuable tool for robust statistical inference and group comparison analysis.