Quantiles underpin widely used tools in finance, insurance, and economic inequality—yet building statistical inference for quantiles can be challenging because empirical quantiles are order statistics rather than simple averages. In a new study published in Risk Sciences , a team of researchers developed a general, nonparametric statistical inference theory for integrals of quantiles (also referred to as integrated quantiles).
A key feature of the work is that its conditions are expressed in terms of general approximating sequences of cumulative distribution functions (cdfs), and are not attached to any specific sampling design or dependence structure, allowing the results to be adapted to different data settings.
To make the theory easier to connect with familiar settings, the team illustrated the results using simple random sampling and discussed how the framework can be used with dependent data such as time series.
The authors also highlight how the developed theory yields unified large-sample arguments for a range of classical estimators (including trimmed means) and offers insight into why various conditions appear in asymptotic results.As the authors write: "We have developed a general statistical inference theory for integrals of quantiles." They add that the work discusses "consistency, bias, and asymptotic normality of various integrals of quantiles and their combinations that arise in risk and economic-inequality measurements," including "the upside and downside tail-values-at-risk … and the Lorenz and Gini curves."
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Contact the author:
Ričardas Zitikis, Western University (Canada)
rzitikis@uwo.ca
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Risk Sciences
Data/statistical analysis
Not applicable
Fundamentals of non-parametric statistical inference for integrated quantiles
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.