Reference priors in multiparameter nonregular cases

The reference prior in the sense of Bernardo is derived in some multiparameter nonregular cases. The family of densities we consider have discontinuities at some points which depend on one component of the parameter (say, theta) while, for fixed values of theta, the family is regular with respect to the other components (say, phi). We obtain the reference prior through an asymptotic expansion of Lindley's measure of information. The expansion is in itself of some importance. The results are illustrated using examples.