A phase I change‐point method for high‐dimensional process with sparse mean shifts

Although Phase I analysis of multivariate processes has been extensively discussed, the discussion on techniques for Phase I monitoring of high‐dimensional processes is still limited. In high‐dimensional applications, it is common to observe that a large number of components but only a limited number of them change at the same time. The shifted components are often sparse and unknown a priori in practice. Motivated by this, this article studies Phase I monitoring of high‐dimensional process mean vectors under an unknown sparsity level of shifts. The basic idea of the proposed monitoring scheme is to first employ the false discovery rate procedure to estimate the sparsity level of mean shifts, and then to monitor the mean changes based on the maximum of the directional likelihood ratio statistics over all the possible shift directions. The comparison results based on extensive simulations favor the proposed monitoring scheme. A real example is presented to illustrate the implementation of the new monitoring scheme.