Empirical evolution equations
Susan Wei, Victor M Panaretos
ELECTRONIC JOURNAL OF STATISTICS | INST MATHEMATICAL STATISTICS | Published : 2018
Evolution equations comprise a broad framework for describing the dynamics of a system in a general state space: when the state space is finite-dimensional, they give rise to systems of ordinary differential equations; for infinite-dimensional state spaces, they give rise to partial differential equations. Several modern statistical and machine learning methods concern the estimation of objects that can be formalized as solutions to evolution equations, in some appropriate state space, even if not stated as such. The corresponding equations, however, are seldom known exactly, and are empirically derived from data, often by means of nonparametric estimation. This induces uncertainties on the ..View full abstract
This research was partly supported by a European Research Council Starting Grant to Victor M. Panaretos. We acknowledge Tomas Rubin for helpful comments on an earlier draft. Finally, we are grateful to the Associate Editor and two referees for their insights.