Date of Award
12-1-2025
Degree Name
Doctor of Philosophy
Department
Mathematics
First Advisor
Olive, David
Abstract
Consider testing the hypothesis $H_0: mu = zero$ versus $H_A: mu is not = zero$using a random sample $x_1, ..., x_n$ where the $x_i$ are p times1 random vectors and p may be much larger than n. Several one sample tests use the same test statistic T_n with different estimators of the variance V(T_n). Rather simple theory from U-statistics is used to find V(T_n), resulting in an estimator that is quick to compute when $H_0$ is true. Some two sample tests for $H_0: mu_1 = mu_2$ are also considered.
Access
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