A high-dimensional bias-corrected AIC for selecting response variables in multivariate calibration

In a multivariate linear regression with a p-dimensional response vector y and a q-dimensional explanatory vector x, we consider a multivariate calibration problem requiring the estimation of an unknown explanatory vector corresponding to a response vector based on and n-samples of x and y. We propose a high-dimensional bias-corrected Akaike's information criterion () for selecting response variables. To correct the bias between a risk function and its estimator, we use a hybrid-high-dimensional asymptotic framework such that n tends to but p/n does not exceed 1. Through numerical experiments, we verify that the performs better than a formal AIC.