Department of Statistics, Faculty of Sciences, Dokuz Eylül University, İzmir, Turkey.
Br J Math Stat Psychol. 2020 Nov;73(3):506-521. doi: 10.1111/bmsp.12198. Epub 2020 Jan 16.
Quantiles are widely used in both theoretical and applied statistics, and it is important to be able to deploy appropriate quantile estimators. To improve performance in the lower and upper quantiles, especially with small sample sizes, a new quantile estimator is introduced which is a weighted average of all order statistics. The new estimator, denoted NO, has desirable asymptotic properties. Moreover, it offers practical advantages over four estimators in terms of efficiency in most experimental settings. The Harrell-Davis quantile estimator, the default quantile estimator of the R programming language, the Sfakianakis-Verginis SV2 quantile estimator and a kernel quantile estimator. The NO quantile estimator is also utilized in comparing two independent groups with a percentile bootstrap method and, as expected, it is more successful than other estimators in controlling Type I error rates.
分位数在理论和应用统计学中都有广泛的应用，因此能够使用适当的分位数估计量非常重要。为了提高下限和上限分位数的性能，特别是在样本量较小时，引入了一种新的分位数估计量，它是所有顺序统计量的加权平均值。新的估计量，记为 NO，具有理想的渐近性质。此外，与 R 编程语言中的默认分位数估计量 Harrell-Davis 分位数估计量、Sfakianakis-Verginis SV2 分位数估计量和核分位数估计量相比，它在大多数实验设置下具有效率方面的实际优势。NO 分位数估计量还用于使用百分位自举方法比较两个独立组，并且如预期的那样，它在控制第一类错误率方面比其他估计量更成功。
