##Statistics Seminar##\\ Department of Mathematical Sciences
^ **DATE:**|Thursday, Oct. 1, 2020 |
^ **TIME:**|1:15pm -- 2:15pm |
^ **LOCATION:**|Zoom Meeting |
^ **SPEAKER:**|Yishi Wang, University of North Carolina Wilmington University |
^ **TITLE:**|Inference of a two-sample order free trend test |
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**Abstract**
A new nonparametric methodology is developed for testing whether two independent
groups sharing the same changing pattern from a response variable, over multiple
ordered sub-populations in each of the two groups. The question is formalized into a
nonparametric two-sample comparison problem for the stochastic order among
subsamples, through U-statistics with accommodations for zero-inflated
distributions. A novel bootstrap procedure is proposed to obtain the critical values
with given type I error. Following the procedure, bootstrapped p-values are obtained
through simulated samples. It is proven that the distribution of the test statistics
is independent from the underlying distributions of the subsamples, when certain
sufficient statistics provided. Furthermore, this study also develops a feasible
framework for power studies to determine sample sizes, which is necessary in
real-world applications. Simulation results suggest that the test is consistent. The
methodology is illustrated using a biological experiment with a split-plot design,
and significant differences in changing patterns of seed weight between treatments
are found with relative small subsample sizes. The asymptotic distribution of the
test is also investigated.