Asymptotic Stability of Emphirical Processes and related Functionals, February 2019

José L. Fernández, Enrico Ferri, Carlos Vázquez: Let E be a space of observables in a sequence of trials Epsilon_n and define m_n to be the empirical distributions of the outcomes. We discuss the almost sure convergence of the sequence m_n in terms of the psi-weak topology of measures, when the sequence Epsilon_n is assumed to be stationary. In this respect, the limit variable is naturally described as a certain canonical conditional distribution. Then, given some functional tau defined on a space of laws, the consistency of the estimators tau(m_n) is investigated. Moreover, a result on the asymptotic stability of the distribution of tau(m_n) w.r.t. certain transformations of the data is given.
Please click here to download the PDF.

application/pdf ffv_jma.pdf — 348 KB