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Asymptotic Expansions for Several GEL-Based Test Statistics and Hybrid Bartlett-Type Correction with Bootstrap

In: Research Papers in Statistical Inference for Time Series and Related Models

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  • Yoshihide Kakizawa

    (Hokkaido University, Kita-ku, Sapporo)

Abstract

This paper mainly discusses two issues about asymptotic expansions for the distributions of $$\chi ^2$$ χ 2 -type test statistics. First, it is shown that the generalized empirical likelihood ratio, Wald-type, and score-type test statistics for a subvector hypothesis in the possibly over-identified moment restrictions are, in general, not Bartlett-correctable, except for the empirical likelihood ratio test statistic. Second, starting with the classical likelihood or the modern generalized empirical likelihood, the Bartlett-type corrected test statistics, with the bootstrap procedure, are proposed to achieve a higher-order accurate testing inference for the nonparametric setup as well as the parametric setup.

Suggested Citation

  • Yoshihide Kakizawa, 2023. "Asymptotic Expansions for Several GEL-Based Test Statistics and Hybrid Bartlett-Type Correction with Bootstrap," Springer Books, in: Yan Liu & Junichi Hirukawa & Yoshihide Kakizawa (ed.), Research Papers in Statistical Inference for Time Series and Related Models, chapter 0, pages 247-289, Springer.
    • Handle: RePEc:spr:sprchp:978-981-99-0803-5_10
    DOI: 10.1007/978-981-99-0803-5_10
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