Abstract :
For a one parameter parametric family {Pθ, θεΩ R1} we study the total variation distance, D, between the unknown distribution Pθ0, and the estimated distribution , where is the maximum likelihood estimator of θ0 based on a sample x1,…, xn from Pθ0. Knowledge of the distribution of D yields simultaneous confidence intervals for {Pθ0(A), Aεβ} where β is the class of Borel sets in R1. In the case of a normal distribution with known variance the exact distribution is obtained. More generally the asymptotic distribution of √nD is derived and explicitly computed for several families of interest. For θ an m vector, m 2, an asymptotically conservative set of confidence intervals for {Pθ0(A), Aεβ} os constructed.
