Interval estimators for ratios of independent quantiles and interquantile ranges

Abstract

Recent research has shown that interval estimators with good coverage properties are achievable for some functions of quantiles, even when sample sizes are not large. Motivated by this, we consider interval estimators for the ratios of independent quantiles and interquantile ranges that will be useful when comparing location and scale for two samples. Simulations show that the intervals have excellent coverage properties for a wide range of distributions, including those that are heavily skewed. Examples are also considered that highlight the usefulness of using these approaches to compare location and scale.

Robust analogs to the Coefficient of Variation

“…First, we introduce asymptotic Wald-type intervals using the asymptotic standard errors from earlier. With recent results highlighting very good coverage for estimators based on ratios of quantiles even for small samples (Prendergast & Staudte, 2016b, 2017aArachchige et al , 2019), we are confident of similarly good coverage for RCV Q . We also propose an asymptotic interval for RCV M as well as bootstrap intervals.…”

“…We selected three pairs of suburbs which were considered by (Arachchige et al , 2019) to calculate the interval estimators for ratios CV, RCV Q and RCV M to assess differences in relative spread of house prices. and the interval is wide.…”

“…Therefore, given the obvious need for interval estimators that has attracted the interest for many others, one aim of this paper is to provide reliable interval estimators. We are motivated to do so by noting the excellent coverage achieved for measures based on ratios of quantiles, even for small samples (Prendergast & Staudte, 2016b, 2017aArachchige et al , 2019).…”

Distribution-Free Confidence Intervals for Functions of Quantiles

“…The thesis consists of four papers [1][2][3][4], which had been either published or submitted at the time of thesis submission, and also includes some introductory material.…”

“…In [1], the distribution-free point and interval estimators were introduced for ratios of independent quantiles to compare the locations of two independent samples. The interquantile range, which is the most natural quantile-based estimator of scale, was used to compare the scales of two independent samples.…”