|
Abstract:
|
A common problem arising when analyzing high-dimensional or functional data is that estimates of the covariance are not of full rank, resulting in the inverse being degenerate. Munk et al. (2008) applied the idea of a neighborhood hypothesis test to the one- and multi-sample problems for functional data by deriving a test statistic to determine whether a group of means are approximately equal. More precisely, they tested whether the means were within a predetermined distance to each other. Unfortunately, in many applications, this pre-determined distance is difficult to both specify and interpret. In this presentation, we present a modified test for determining whether the distance between a mean and a hypothesized function is less than a proportion of the total population variance. We will derive a test statistic that is asymptotically normal, and present both simulation studies of the power of the procedure and an application to a data set arising from ecology.
|
