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Relative Error Accurate Statistic Based on Nonparametric Likelihood

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  • Lorenzo Camponovo

    (University of Surrey)

  • Taisuke Otsu

    (London School of Economics)

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.

Suggested Citation

  • Lorenzo Camponovo & Taisuke Otsu, 2018. "Relative Error Accurate Statistic Based on Nonparametric Likelihood," School of Economics Discussion Papers 0518, School of Economics, University of Surrey.
    • Handle: RePEc:sur:surrec:0518
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    File URL: https://repec.som.surrey.ac.uk/2018/DP05-18.pdf
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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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