Relative Error Accurate Statistic Based on Nonparametric Likelihood

Lorenzo Camponovo and Taisuke Otsu
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Lorenzo Camponovo: University of Surrey
Taisuke Otsu: London School of Economics

No 518, School of Economics Discussion Papers from School of Economics, University of Surrey

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 function 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 is asymptotically chi-squared distributed with a relative error 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 over-identified moment condition models.

Pages: 15 pages
Date: 2018-02
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https://repec.som.surrey.ac.uk/2018/DP05-18.pdf (application/pdf)

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Working Paper: Relative error accurate statistic based on nonparametric likelihood (2017)
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Persistent link: https://EconPapers.repec.org/RePEc:sur:surrec:0518

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