Estimation in a model with infinite-dimensional nuisance parameter

Let X1 be a random variable with density function f(t) Ψ(t) be an increasing absolutely continuous function Φ(t) be the inverse function to Ψ(t) and X2 be the random variable X2 = Φ(X1). We consider the maximum likelihood estimator for the density ψ of the function Ψ in the case when we observe two independent samples from the distributions of X1 and X2. Under appropriate conditions on the involved distributions we prove the consistency of the maximum likelihood estimator. Bibliography: 1 title. © 2006 Springer Science+Business Media, Inc.