A note on testing complete independence for high dimensional data

The high dimensional independence test in Schott (2005) assumes (m,n)→∞(m,n)→∞ and mn→γ∈(0,∞), where mm signifies the dimension and nn denotes the sample size. This paper notes that without the restriction mn→γ, the test is still effective provided that (m,n)→∞(m,n)→∞, or nn is fixed but m→∞m→∞.