Seminario: "Bivariate splines for spatial functional data"

Fecha: Viernes, 17 de mayo de 2013
Lugar: Facultad de Ciencias. Aula A14
Horario: 10:00 h.
Descripción:
Seminario impartido por el Profesor Serge Guillas (Department of Statistical Science University College London)
- Abstract: First, we consider the functional linear regression model where the explanatory variable is a random surface and the response is a real random variable, in various situations where both the explanatory variable and the noise can be unbounded and dependent. Bivariate splines over triangulations represent the random surfaces. We use this representation to construct least squares estimators of the regression function with a penalization term. Under the assumptions that the regressors in the sample span a large enough space of functions, bivariate splines approximation properties yield the consistency of the estimators. Simulations demonstrate the quality of the asymptotic properties on a realistic domain. We also carry out an application to ozone concentration forecasting over the USA that illustrates the predictive skills of the method. We compare the least squares method with penalty to the principal components regression approach. Moderate sample sizes provide good quality forecasts in both cases with little computational effort. We also illustrate the variability of forecasts owing to the choice of smoothing penalty. Finally, we compare our predictions with the ones obtained using thin-plate splines. Predictions based on bivariate splines require less computational time than the ones based on thin-plate splines, are more accurate, and exhibit more robustness to variations in sampling.
  Secondly, we consider the estimation of a non-negative surface over a complex domain with an irregular boundary and interior holes. We employ bivariate splines over triangulations to build the surface. Then non-negativity condition can be satisfied by recasting the estimation of the spline’s coefficients as a constrained penalized least squares problem over the spline basis. In addition, boundary conditions are enforced in accordance with the given application.
  In the absence of replicates of a given surface, the computation of spatial uncertainties in the estimation is here addressed by bootstrapping the original surface. As a result, we compute and display boxplots for the distribution of surfaces that rely on functional data depth. An illustration to the estimation of population density of a town separated by a river highlights the skills of the method.
Organiza: Máster Oficial en Estadística Aplicada y el Programa Oficial de Doctorado en Matemáticas y Estadística. Proyecto MTM2012-32674.
Más información: Maria D. Ruiz Medina
Catedrática de Universidad
Departamento de Estadistica e Investigacion Operativa
Universidad de Granada
Campus Fuente Nueva s/n
E-18071 Granada
Spain
Phone: (34) 958 243270
Fax: (34) 958 243267
E-mail: mruiz@ugr.es

Seminario: «Bivariate splines for spatial functional data»

17 mayo 2013 | 08:00 - 09:00 h

Actividades culturales y de divulgación
Conferencias, seminarios, divulgación científica

Fechas y horarios

Seminario: «Bivariate splines for spatial functional data»

17 mayo 2013 | 08:00 - 09:00 h

Actividades culturales y de divulgaciónConferencias, seminarios, divulgación científica

Fechas y horarios

Actividades culturales y de divulgación
Conferencias, seminarios, divulgación científica