Relative Error Accurate Statistic Based on Nonparametric Likelihood

Lorenzo Camponovo, Yukitoshi Matsushita, Taisuke Otsu

Research output: Contribution to journalArticlepeer-review


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 both in normal and large deviation regions. Numerical results illustrate the accuracy of the proposed TET statistic. Our results cover both just- A nd 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.

Original languageEnglish
Pages (from-to)1214-1237
Number of pages24
JournalEconometric Theory
Issue number6
Publication statusPublished - 2021 Dec 1
Externally publishedYes

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Economics and Econometrics


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