We introduce the so-called naive tests and give a brief review of the new developments. Naive testing methods are easy to understand and perform robustly, especially when the dimension is large. We focus mainly on reviewing some naive testing methods for the mean vectors and covariance matrices of high-dimensional populations, and we believe that this naive testing approach can be used widely in many other testing problems.
@cite_10 proposed another statistic: which is called the regularized Hotelling @math test. The idea is to employ the technique of ridge regression to stabilize the inverse of the sample covariance matrix given in ). Assuming that the underlying distribution is normally distributed, it is proven that under the null hypothesis, for any @math , as @math where @math and @math . They also give an asymptotic approximation method for selecting the tuning parameter @math in the regularization. Recently, based on a supervised-learning strategy, Shen and Lin @cite_5 proposed a statistic to select an optimal subset of features to maximize the asymptotic power of the Hotelling @math test.
@cite_5 @cite_10
2120633692 2022771765
The problem of testing the mean vector in a high-dimensional setting is considered. Up to date, most high-dimensional tests for the mean vector only make use of the marginal information from the variables, and do not incorporate the correlation information into the test statistics. A new testing procedure is proposed, which makes use of the covariance information between the variables. The new approach is novel in that it can select important variables that contain evidence against the null hypothesis and reduce the impact of noise accumulation. Simulations and real data analysis demonstrate that the new test has higher power than some competing methods proposed in the literature. Recent proteomic studies have identified proteins related to specific phenotypes. In addition to marginal association analysis for individual proteins, analyzing pathways (functionally related sets of proteins) may yield additional valuable insights. Identifying pathways that differ between phenotypes can be conceptualized as a multivariate hypothesis testing problem: whether the mean vector μ of a p-dimensional random vector X is μ0. Proteins within the same biological pathway may correlate with one another in a complicated way, and Type I error rates can be inflated if such correlations are incorrectly assumed to be absent. The inflation tends to be more pronounced when the sample size is very small or there is a large amount of missingness in the data, as is frequently the case in proteomic discovery studies. To tackle these challenges, we propose a regularized Hotelling’s T2 (RHT) statistic together with a nonparametric testing procedure, which effectively controls the Type I error rate and maintains ...