RELATIVE ERROR ACCURATE STATISTIC BASED ON NONPARAMETRIC LIKELIHOOD

This paper develops a new test statistic for parameters defined by moment conditions that exhibits desirable relative error properties the approximation of tail area probabilities. Our statistic, called tilted exponential tilting (TET) is constructed estimating certain cumulant generating functions under weights. We show asymptotic p -value TET can provide an accurate to infeasible saddlepoint which admits Lugannani–Rice style adjustment with errors order $n^{-1}$ both in normal and large deviation regions. Numerical results illustrate accuracy proposed statistic. cover just- overidentified condition models. A limitation our analysis theoretical are exclusively closeness -values ones feasible only numerically assessed.