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<p>Quantiles are important in statistics and widely used in various fields such as social and economic studies. In recent years, more and more attention has been paid to high-frequency data. In this paper, we construct confidence intervals (CIs) for quantiles of a population under strong mixing high-frequency data by using blockwise empirical likelihood (EL) method. It is shown that the blockwise EL ratio statistic is asymptotically <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42952_2025_319_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(\chi ^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>χ</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-type distributed, which is used to construct CIs for quantiles. In addition, results of a simulation study on the finite sample performance of the CIs are reported, while an empirical analysis for the applications of theoretical results is presented. We compare the performance of CIs based on the EL method with those constructed by the normal approximation (NA) method in our simulations. Simulation results show that CIs based on the EL method outperform those based on the NA method.</p>

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Empirical likelihood for quantiles under strong mixing high-frequency data

  • 期刊论文

  • 发表日期：

    2025年3月27日

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  • Wenjing Tang,
  • Yongsong Qin

摘要

Quantiles are important in statistics and widely used in various fields such as social and economic studies. In recent years, more and more attention has been paid to high-frequency data. In this paper, we construct confidence intervals (CIs) for quantiles of a population under strong mixing high-frequency data by using blockwise empirical likelihood (EL) method. It is shown that the blockwise EL ratio statistic is asymptotically \(\chi ^2\) χ 2 -type distributed, which is used to construct CIs for quantiles. In addition, results of a simulation study on the finite sample performance of the CIs are reported, while an empirical analysis for the applications of theoretical results is presented. We compare the performance of CIs based on the EL method with those constructed by the normal approximation (NA) method in our simulations. Simulation results show that CIs based on the EL method outperform those based on the NA method.