Asymptotic inference for spatial CDFS over time

A spatial cumulative distribution function (SCDF) is a random function that provides a statistical summary of a random process over a spatial domain of interest. In this paper, we consider a spatio-temporal process and establish statistical methodology to analyze changes in the SCDF over time. We develop hypothesis testing to detect a difference in the spatial random processes at two time points, and we construct a prediction interval to quantify such discrepancy in the corresponding SCDFs. Using a spatial subsampling method, we show that our inferences are valid asymptotically. As an illustration, we apply these inference procedures to test and predict changes in the SCDF of an ecological index for foliage condition of red maple trees in the state of Maine in the early 1990s.