6. Statistics of Sparsely Sampled Curves

We develop new statistical methods for analyzing sparsely sampled curves that vary in time. The typical dataset is differences in log gene expressions from case-control pairs for a large number of genes sampled relative to time of diagnosis. We focus on weak signals in the gene expression in many genes instead of strong signals in a few genes. The methods are based on moving windows in time, hypothesis testing, dimension reductions and randomization of the time to observa-tion.