Functional ANOVA starting from discrete data: an application to air quality data

A nonparametric functional approach is proposed to compare the mean functions of $k$ k samples of curves. In practice, curves data are usually collected in a discrete form and hence they must be pre-processed to use purely functional techniques. However, in the context of $k$ k -sample tests, the pre-processing step can have effects in terms of power reduction. Hall and Van Keilegom (Stat Sin 17:1511–1531, 2007) proposed a methodology to minimizing these effects in the context of tests for the equality of two distribution functions. Their procedure is here extended to the case of $k$ k -sample hypothesis tests. The asymptotic validity of the procedure is established and its finite sample performance is analyzed through Monte Carlo experiments. As an illustration, the method is applied to air quality data collected from several monitoring stations placed at different geographical locations at the center of Spain.