Bivariate splines for ozone concentration predictions

Abstract

For ground level ozone prediction, we consider a functional linear regression model where the explanatory variable is a real random surface and the response is a real random variable. We use bivariate splines over triangulations to represent the random surfaces. Then we use this representation to construct two solutions, a least squares estimate of the regression function based on a brute force approach, and an autoregressive estimator based on a principal component analysis. We apply these two functional linear models to ground level ozone forecasting over the United States to illustrate the predictive skills of these two methods. We also extend the brute force approach to a model where both the explanatory variable and the response are both real random surfaces.