The performances of four quantile estimators when comparing dependent groups with a percentile bootstrap method

12th International Statistics Days Conference - ISDC2022, İzmir, Türkiye, 13 - 16 Ekim 2022, ss.59

Comparing two dependent groups is an essential research topic in applied statistics. When

doing this, the location measures of the marginal distributions are generally used to compare

before and after measurements derived from the same sample group. The location estimators,

especially the mean, are generally sensitive to outlying observations. So if the point of interest

is the tails of the marginal distributions, location measures might not provide deep insight,

and a more specific measurement might be needed. Quantiles are reference values intended

to reflect the typical observations of a given particular point of a distribution. There are three

main approaches for obtaining a quantile estimator: using a single order statistic, taking the

weighted average of two order statistics, and taking the weighted average of all order

statistics. A common problem for all quantile estimators is getting a reasonable accurate

standard error estimation and a hypothesis testing procedure for the corresponding

population parameter. The percentile bootstrap approach in hypothesis testing performs

reasonably well in simulations. In this study, the newly proposed NO quantile estimator, the

Harrell-Davis quantile estimator, the trimmed Harrell-Davis quantile estimator, and the

default quantile estimator in R function quantile() (type-7 quantile estimator) were used to

compare the different quantile values of the two dependent groups using the percentile

bootstrap method. The study aims to compare the performances of four different quantile

estimators in terms of saving Type I error for the 0.05 level. A simulation design was

conducted for varying correlations, quantile values, sample sizes, and targeted statistical

distributions. All computations were performed in R 4.2. It was found that the NO quantile

estimator gives better results than the other quantile estimators in most of the scenarios

covered.

Keywords: no quantile estimator, percentile bootstrap method, two dependent groups