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<p>The wide application of high-frequency data has attracted the in-depth research of scholars in various fields, especially in econometrics and statistics. In this article, we construct a blockwise empirical likelihood (EL) ratio statistic for a nonparametric regression function under <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="362_2025_1683_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\rho \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ρ</mi> </math></EquationSource> </InlineEquation>-mixing high-frequency data and show that the blockwise EL ratio statistic is asymptotically <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="362_2025_1683_Article_IEq4.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. The asymptotic confidence interval (CI) for the nonparametric regression function based on the blockwise EL approach is thus given. The results of a simulation study on the finite sample performance of the CIs are presented. At the same time the theoretical findings are applied to a real data analysis. Numerical simulation results show that the CIs constructed by the blockwise EL method perform better than those constructed by the normal approximation method.</p>

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Empirical likelihood for nonparametric regression functions under \(\rho \)-mixing high-frequency data

  • 期刊论文

  • 发表日期：

    2025年3月13日

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  • Wenjing Tang,
  • Yongsong Qin

摘要

The wide application of high-frequency data has attracted the in-depth research of scholars in various fields, especially in econometrics and statistics. In this article, we construct a blockwise empirical likelihood (EL) ratio statistic for a nonparametric regression function under \(\rho \) ρ -mixing high-frequency data and show that the blockwise EL ratio statistic is asymptotically \(\chi ^2\) χ 2 -type distributed. The asymptotic confidence interval (CI) for the nonparametric regression function based on the blockwise EL approach is thus given. The results of a simulation study on the finite sample performance of the CIs are presented. At the same time the theoretical findings are applied to a real data analysis. Numerical simulation results show that the CIs constructed by the blockwise EL method perform better than those constructed by the normal approximation method.