Asymptotic equivalence for a model of independent non identically distributed observations

Abstract It is shown that a nonparametric model of independent non identically distributed observations on the unit interval can be approximated, in the sense of Le Cam´s Δ-distance, by a bivariate Gaussian white noise model. The parameter space is a smoothness class of conditional densities uniformly bounded away from zero on the unit square. The proof is based on coupling of likelihood processes via a functional Hungarian construction of the sequential empirical process and the Kiefer–Müller process.