Semiparametric Bayesian and Frequentist Tests of Trend
for a Large Collection of Variable Stars
Jeffrey D. Hart
Texas A&M University
Several nonparametric and/or smoothing-based techniques for testing the fit of parametric regression models are reviewed. Most of these tests are frequentist in nature, but Bayesian tests and their frequentist properties are also discussed. Strengths and weaknesses of the various methods are discussed in the context of testing the ``no-effect'' hypothesis. The tests are then illustrated by applying them to astronomical data. The data are observed lengths of time, or periods, between maxima on the light curves of variable stars. Astronomers
are interested in detecting trends in such a sequence of periods. The model for the periods is semiparametric: nonparametric for the average periods and parametric for the error series. The issue of false discovery rate is addressed.