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RELATIVE ERROR ACCURATE STATISTIC BASED ON NONPARAMETRIC LIKELIHOOD

Published online by Cambridge University Press:  01 March 2021

Lorenzo Camponovo ,
Yukitoshi Matsushita  and
Taisuke Otsu
Lorenzo Camponovo
Affiliation:
University of Applied Sciences and Arts of Italian Switzerland
Yukitoshi Matsushita
Affiliation:
Hitotsubashi University
Taisuke Otsu*
Affiliation:
London School of Economics
*
Address correspondence to Taisuke Otsu, Department of Economics, London School of Economics, Houghton Street, London WC2A 2AE, UK; e-mail: t.otsu@lse.ac.uk.
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Abstract

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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.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 6 , December 2021 , pp. 1214 - 1237
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Footnotes

We gratefully acknowledge support from the JSPS KAKENHI (18K01541; Matsushita) and the ERC Consolidator Grant (SNP 615882; Otsu). We would like to thank Elvezio Ronchetti and Richard Spady for their helpful discussions and seminar participants at the University of Geneva for their comments. We would also like to thank the Editor, a Co-Editor, and anonymous referees for their helpful comments.

References

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