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Econometrics Paper
Relative error accurate statistic based on nonparametric likelihood
Lorenzo Camponovo and Taisuke Otsu
November 2017
Paper No' EM 593:
Full Paper (pdf)

JEL Classification: C12; C14

Tags: nonparametric likelihood; saddlepoint; moment condition model

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.