Asymptotic properties of functional maximum-likelihood ARH parameter estimators
Abstract
In this paper, the asymptotic distribution of the maximum likelihood functional estimators of the operators involved in the formulation of gaussian ARH(1) models is studied in the case of imcomplete functional data (see Ruiz-Medina and Salmerón, 2009, Ruiz-Medina, Salmerón and Angulo, 2007, and Salmerón and Ruiz-Medina, 2009). Specifically, an extension to the functional context of the Titterington (1983, 1984) results is derived by applying a Robbins-Monro-type invariance procedure. The asymptotic properties of the functional predictors computed by applying Kalman filtering are then obtained from a functional version of Bosq (2008) results.