TEST OF SIGNIFICANCE WHEN DATA ARE CURVES

With modern technology, massive data can easily be collected in a form of multiple sets of curves. New statistical challenge includes testin g whether there is any statistically significant difference among thes e sets of curves. In this article we propose some new tests for compar ing two groups of curves based on the adaptive Neyman test and the wav elet thresholding techniques introduced earlier by Fan. We demonstrate that these tests inherit the properties outlined by Fan and that they are simple and powerful for detecting differences between two sets of curves. We then further generalize the idea to compare multiple sets of curves, resulting in an adaptive high-dimensional analysis of varia nce, called HANOVA. These newly developed techniques are illustrated b y using a dataset on pizza commercials where observations are curves a nd an analysis of cornea topography in ophthalmology where images of i ndividuals are observed. A simulation example is also presented to ill ustrate the power of the adaptive Neyman test.