Rank tests for PCA under weak identifiability
弱可识别条件下主成分分析的秩检验
In a triangular array framework where n observations are randomly sampled from a p-dimensional elliptical distribution with shape matrix Vn, we consider the problem of testing the null hypothesis H0:θ=θ0 against the alternative hypothesis H1:θ≠θ0, where θ is the (fixed) leading unit eigenvector of Vn and θ0 is a given unit p-vector. The dependence of the shape matrix on the sample size allows us to consider challenging asymptotic scenarios in which the parameter of interest…