Testing the mean and variance by e-processes
针对非平稳数据，研究如何检验条件均值和条件方差，构建了四种非参数复合假设的e值和p值，并通过e过程（即赌注检验）构造检验方法，模拟和实证研究展示了其特点。
Summary We address the problem of testing the conditional mean and conditional variance for nonstationary data. We build e-values and p-values for four types of nonparametric composite hypothesis with specified mean and variance as well as other conditions on the shape of the data-generating distribution. These shape conditions include symmetry, unimodality and their combination. Using the obtained e-values and p-values, we construct tests via e-processes, also known as testing by betting, as well as some tests based on combining p-values for comparison. Although we mainly focus on one-sided tests, the two-sided test for the mean is also studied. Simulation and empirical studies are conducted under a few settings, and they illustrate features of the methods based on e-processes.