Distribution-free tests for no effect of treatment in heteroscedastic functional data under both weak and long range dependence

In this paper, we present distribution-free tests to evaluate the effect of multiple treatments when there are a large number of repeated measurements from each subject nested in a treatment. We formulate new test statistics to account for heteroscedasticity and unbalanced designs. The asymptotic distributions for the test statistics are obtained when the repeated measurements from the same subject have long range dependence and weak dependence, respectively. The asymptotic results hold under the nonclassical setting in which the number of repeated measurements is large while the number of subjects per treatment may be small. A real application to compare cattle ear temperature profiles under different antibiotic treatments is given for illustration. Simulation studies are undertaken to compare the empirical performance of the proposed tests to commonly used methods.