Bivariate splines for ozone concentration forecasting

Abstract

In this paper, we forecast ground level ozone concentrations over the USA, using past spatially distributed measurements and the functional linear regression model. We employ bivariate splines defined over triangulations of the relevant region of the USA to implement this functional data approach in which random surfaces represent ozone concentrations. 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 and are more accurate. We also quantify the variability in the predictions arising from the variability in the sample using the jackknife, and report that predictions based on bivariate splines are more robust than the ones based on thin‐plate splines. Copyright © 2012 John Wiley & Sons, Ltd.

Bivariate splines for spatial functional regression models

“…In particular, they are consistent for various learning periods. For more experimental results based on various size of triangulations and regions, see Ettinger (2009).…”

Efficiency in multivariate functional nonparametric models with autoregressive errors

“…Neighboring stations should contain additional information on each other. A joint modeling is possible, as shown in Ettinger et al (2012). Time series of random surfaces at one particular hour of ozone are used in that paper to predict a particular hour at one location the day after.…”

Some first results on the consistency of spatial regression with partial differential equation regularization

“…It should be pointed out that the problem of analyzing data spatially distributed over irregularly shaped two-dimensional domains has recently attracted an increasing interest, and other regularized least-square smoothers have been proposed that can tackle this issue, such as bivariate splines over triangulations [see, e.g., Lai and Schumaker, 2007, Guillas and Lai, 2010, Ettinger et al, 2012, Lai and Wang, 2013, soap film smoothing [Wood et al, 2008], and low-rank thin-plate spline approximations Ranalli, 2007, Scott-Hayward et al, 2014]. All these methods have isotropic and stationary regularizing terms; bivariate splines over triangulations can include high order derivatives.…”