English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we derive the joint asymptotic distributions of functions ofquantile estimators (the non-parametric sample quantile and the parametriclocation-scale quantile estimator) with functions of measure of dispersionestimators (the sample variance, sample mean absolute deviation, sample medianabsolute deviation) - assuming an underlying identically and independentlydistributed sample. We also discuss the conditions required by the use of suchestimators. Further, we show that these results can be extended to any higherorder absolute central sample moment as measure of dispersion. Aware of thedifference in speed of convergence of the two quantile estimators, we comparethe impact of the choice of the quantile estimator (and measure of dispersion)on the asymptotic correlations. Then we prove a scaling law for the asymptoticdependence of quantile estimators with measure of dispersion estimators.Finally, we show a good finite sample performance of the asymptotics insimulations for elliptical distributions. All the results should constitute animportant and useful complement in the statistical literature as thoseestimators are either of standard use in statistics and application fields, orshould become as such because of weaker conditions in the asymptotic theorems.

On the Dependence between Functions of Quantile and Dispersion Estimators