4 Application: Ozone Pollution Data Ground-level ozone is an air pollutant known to cause serious health problems. Unlike other pollutants, ozone is not emitted directly into the air but forms as a result of complex chemical reactions, including volatile organic compounds and oxides of nitrogen among other factors. Modeling ground-level ozone formation has been an active topic of air- quality studies for many years. The California Environmental Protection Agency database, available at http://www.arb.ca.gov/aqd/aqdcd/aqdcddld.htm, has collected data on hourly concentrations of pollutants at different locations in California for the years 1980 to 2009. Here we will focus on the trajectories of oxides of nitrogen (NOx) and ozone (O3) in the city of Sacramento (site 3011 in the database) between June 6 and August 26 of 2005, which make a total of 82 days (shown in Figure 1). There are a few days with some missing observations (9 in total), but since the method can handle unequal time grids, imputation of the missing data was not necessary. The first step in the analysis is to fit reduced-rank models to t he sample curves. We used cubic B-splines with 7 equally spaced knots every 5 years, and fitted Normal and t$_{1}$ (Cauchy) reduced-rank models with up to 10 principal components. For both the response and the explanatory curves, the leading three components explain at least 85% of the total variability, so we retained these models. The means and the principal components are plotted in Figure 2. There is no substantial difference between the estimators obtained by these models, except perhaps for the mean and the third component of log-NOx (Figures 2 (a) and (g)). With the Normal component scores we computed the Least Squares estimator, obtain- 13