COMPUTABLE ERROR BOUNDS FOR HIGH-DIMENSIONAL APPROXIMATIONS OF AN LR STATISTIC FOR ADDITIONAL INFORMATION IN CANONICAL CORRELATION ANALYSIS

摘要

Let lambda be the LR criterion for testing an additional information hypothesis on a sub-vector of p-variate random vector x and a subvector of q-variate random vector y, based on a sample of size N = n + 1. Using the fact that the null distribution of -(2/N) log lambda can be expressed as a product of two independent. distributions, we first derive an asymptotic expansion as well as the limiting distribution of the standardized statistic T of -(2/N) log lambda under a high-dimensional framework when the sample size and the dimensions are large. Next, we derive computable error bounds for the high-dimensional approximations. Through numerical experiments it is noted that our error bounds are useful in a wide range of p, q, and n.