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Relative error accurate statistic based on nonparametric likelihood

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  • Camponovo, Lorenzo
  • Matsushita, Yukitoshi
  • Otsu, Taisuke

Abstract

This paper develops a new test statistic for parameters defined by moment conditions that exhibits desirable relative error properties for the approximation of tail area probabilities. Our statistic, called the tilted exponential tilting (TET) statistic, is constructed by estimating certain cumulant generating functions under exponential tilting weights. We show that the asymptotic p-value of the TET statistic can provide an accurate approximation to the p-value of an infeasible saddlepoint statistic, which admits a Lugannani–Rice style adjustment with relative errors of order n −1 both in normal and large deviation regions. Numerical results illustrate the accuracy of the proposed TET statistic. Our results cover both just- and overidentified moment condition models. A limitation of our analysis is that the theoretical approximation results are exclusively for the infeasible saddlepoint statistic, and closeness of the p-values for the infeasible statistic to the ones for the feasible TET statistic is only numerically assessed.

Suggested Citation

  • Camponovo, Lorenzo & Matsushita, Yukitoshi & Otsu, Taisuke, 2021. "Relative error accurate statistic based on nonparametric likelihood," LSE Research Online Documents on Economics 107521, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:107521
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    References listed on IDEAS

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    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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