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<p>The problem of mean testing with inequality constraints plays an important role in statistical inference and practical applications. In recent years, high-frequency data has been attracting increasing attention, and this development has opened up new areas in econometrics and statistics. In this paper, using the blockwise empirical likelihood method, we consider two types of one-sided hypothesis tests for a population mean under inequality constraints and construct the corresponding constrained empirical likelihood (CEL) ratio statistics under <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-mixing high-frequency data, and show that the CEL ratio statistics have the asymptotic distribution <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\frac{1}{2}\chi _0^2 + \frac{1}{2}\chi _1^2,\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msubsup> <mi>χ</mi> <mn>0</mn> <mn>2</mn> </msubsup> <mo>+</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msubsup> <mi>χ</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> from which the rejection regions are determined. Through numerical simulations, we evaluate the finite-sample performance of the CEL method and compare it with the unconstrained empirical likelihood (EL) approach. We also apply the proposed methodology to real data analysis. Simulation and empirical results indicate that the CEL method achieves coverage probabilities closer to the nominal significance level under null hypotheses and have more stable statistical powers, exhibiting superior finite-sample performance and robustness compared with the unconstrained EL method.</p>

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Empirical likelihood test for the mean with inequality constraints under strong mixing high-frequency data

  • 期刊论文

  • 发表日期：

    2026年4月20日

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  • Huiwan Liao,
  • Yinghua Li,
  • Yongsong Qin

摘要

The problem of mean testing with inequality constraints plays an important role in statistical inference and practical applications. In recent years, high-frequency data has been attracting increasing attention, and this development has opened up new areas in econometrics and statistics. In this paper, using the blockwise empirical likelihood method, we consider two types of one-sided hypothesis tests for a population mean under inequality constraints and construct the corresponding constrained empirical likelihood (CEL) ratio statistics under \(\alpha \) α -mixing high-frequency data, and show that the CEL ratio statistics have the asymptotic distribution \(\frac{1}{2}\chi _0^2 + \frac{1}{2}\chi _1^2,\) 1 2 χ 0 2 + 1 2 χ 1 2 , from which the rejection regions are determined. Through numerical simulations, we evaluate the finite-sample performance of the CEL method and compare it with the unconstrained empirical likelihood (EL) approach. We also apply the proposed methodology to real data analysis. Simulation and empirical results indicate that the CEL method achieves coverage probabilities closer to the nominal significance level under null hypotheses and have more stable statistical powers, exhibiting superior finite-sample performance and robustness compared with the unconstrained EL method.