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

Ryoya Oda, Yoshie Mima, Hirokazu Yanagihara and Yasunori Fujikoshi

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 14, 3453-3476

Abstract: 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 x0 corresponding to a response vector y0, based on y0 and n-samples of x and y. We propose a high-dimensional bias-corrected Akaike’s information criterion (HAICC) 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 HAICC performs better than a formal AIC.

Date: 2021
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DOI: 10.1080/03610926.2019.1705978

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