A global consistency result for the two-dimensional Pareto distribution in the presence of misspecified inflation

Abstract

A global consistency result for the ML estimator of a misspecified two-parameter Pareto distribution is proved. The misspecification is due to the assumption of a wrong inflation rate, which violates the i.i.d. assumption in the model. We also investigate how far away from the true parameters one finds the ML estimator of the misspecified model (asymptotically for a small misspecification r). Finally, for the case where the misspecification depends on the number of observations n, i.e., r=r _n , and where $r_{n}\stackrel{n\to \infty}{\longrightarrow}0$, we prove a central limit theorem for the ML estimator.