A conditional composite likelihood ratio test with boundary constraints

Composite likelihood has been widely used in applications. The asymptotic distribution of the composite likelihood ratio statistic at the boundary of the parameter space is a complicated mixture of weighted |$\chi^2$| distributions. In this paper we propose a conditional test with data-dependent degrees of freedom. We consider a modification of the composite likelihood which satisfies the second-order Bartlett identity. We show that the modified composite likelihood ratio statistic given the number of estimated parameters lying on the boundary converges to a simple |$\chi^2$| distribution. This conditional testing procedure is validated through simulation studies.