Multifractional random fields, infinite-dimensional inference and asymptotics in space and time

CICLO DE CONFERENCIAS ESTADÍSTICA Y CIENCIA DE DATOS PATRICIA ROMÁN

Conferenciante: María Dolores Ruiz Medina

Abstract: It is well-known that the concept of random field goes beyond the traditional concept of stochastic process which has been historically conditioned to have a temporal index set. There is no mathematical reason for restricting the parameter and state spaces to be real/complex numbers. Indeed, a stochastic process can also be interpreted as a random element in a space of functions. The denomination random field is applied when the random variables are indexed in a set of the plane, or, in some higher dimensional euclidean space, as well as when the parameter space is a geometric variety. Their values can be functions or any other mathematical objects. Thus, a random field can be viewed as a family of random variables whose indices lie in a topological space and whose values are even in a metric or semimetric space. The present talk reviews several contributions that reveal the flexibility of this concept under the umbrella of multifractionality. In particular, the talk is focused on the statistical modelling and analysis in a space-time framework, going beyond the classical assumptions on local regularity, stationarity and markovianess. Special attention is paid to the infinite-dimensional inference framework. Particularly, some recent advances in functional regression, covering the case of manifold-valued curve process and random fields on manifolds, are reviewed. Some open research lines on space-time aymptotics are also discussed.

Organizadores del ciclo de conferencias: IMAG y el Departamento de Estadística e Investigación Operativa de la Universidad de Granada.