Extended Likelihood Ratio Test Based On Estimating Equations

This article discusses the problem of the simple hypothesis test of unknown parameters when their likelihood is not completely known. We suppose that only first order moment and second order moment are known. In this case, there was a lot of study of point estimation of unknown parameters, these study was use of estimating equations. On this condition, although there was some study of hypothesis test (for example the extended efficient score statistic and extended Wald test statistic), the study was little. In this article, firstly, we discussed the theory of estimating equations, then we obtained the quasi-likelihood of the unknown parameters, finally, the extended likelihood ratio statistic was obtained by use of quasi-likelihood of unknown parameters. So we gain a new test statistic of simple hypothesis when only the first order moment and second moment are known.