Emilio Porcu
University of Newcastle (Upon Tyne, UK) and University Federico Santa Maria Valparaiso (Chile)

Modeling Temporally Evolving and Spatially Globally Dependent Data

18:00- 19:00

Carlos Tenreiro
Universidade de Coimbra

Automatic selection of the tuning parameter appearing in certain families of goodness-of-fit tests

Emilio Porcu. Abstract: The last decades have seen an unprecedented increase in the availability of data sets that are inherently global and temporally evolving, from remotely sensed networks to climate model ensembles. This paper provides a view of statistical modeling techniques for space-time processes, where space is the sphere representing our planet. In particular, we make a distintion between (a) second order-based, and (b) practical approaches to model temporally evolving global processes. The former are based on the specification of a class of space-time covariance functions, with space being the two-dimensional sphere. The latter are based on explicit description of the dynamics of the space-time process, i.e., by specifying its evolution as a function of its past history with added spatially dependent noise. We especially focus on approach (a), where the literature has been sparse. We provide new models of space-time covariance functions for random fields defined on spheres cross time. Practical approaches, (b), are also discussed, with special emphasis on models built directly on the sphere, without projecting the spherical coordinate on the plane. We present a case study focused on the analysis of air pollution from the 2015 wildfires in Equatorial Asia, an event which was classified as the yearâ€™s worst environmental disaster. The paper finishes with a list of the main theoretical and applied research problems in the area, where we expect the statistical community to engage over the next decade.

Carlos Tenreiro Abstract: The situation, common in the current literature, is that of a whole family of location-scale/scale invariant test statistics indexed by a set $\Lambda$ of real numbers, is available to test the goodness of fit of $F$, the underlying distribution function of the real-valued iid random variables $X_1,\dots,X_n$, to a location-scale/scale family of distribution functions. The power properties of the tests associated with the different statistics usually depend on $\lambda\in\Lambda$, called the ``tuning parameter'', which is the reason that its choice is crucial to obtain a performing test procedure. In this talk we address the data-dependent choice of $\lambda$ in the set $\Lambda$, assumed to be finite. Examples of existing and new tuning parameter selectors are discussed, and the methodology presented, of combining different test statistics in a single test procedure, is applied to well known families of test statistics for normality and exponentiality.