Hotelling $$T^2$$ test in high dimensions with application to Wilks outlier method

We consider the Hotelling \(T^2\) test in low sample size, high dimensional setting. We partition the p variables into \(b>1\) blocks of p/b variables and use the union-intersection principle to propose a testing procedure that computes the \(T^2\) test in each block. We show that the proposed method is more powerful than Hotelling \(T^2\) test. We also consider Wilks method of outlier detection and use the union-intersection principle to search for outliers in blocks of variables. The significance level and the power function of the new test are investigated. We show that the new outlier detection method produces more power compared to Wilks test.