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.
https://wakeupcall.project.cwi.nl/research-topics/papers/esr/asymptotic-stability-of-empirical-processes-and-related-functionals.pdf/view
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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.