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

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  • Ryoya Oda
  • Yoshie Mima
  • Hirokazu Yanagihara
  • Yasunori Fujikoshi

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.

Suggested Citation

  • Ryoya Oda & Yoshie Mima & Hirokazu Yanagihara & Yasunori Fujikoshi, 2021. "A high-dimensional bias-corrected AIC for selecting response variables in multivariate calibration," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(14), pages 3453-3476, July.
    • Handle: RePEc:taf:lstaxx:v:50:y:2021:i:14:p:3453-3476
    DOI: 10.1080/03610926.2019.1705978
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    Cited by:

    1. Shengfei Tang & Yanmei Shi & Qi Zhang, 2023. "Bias-Corrected Inference of High-Dimensional Generalized Linear Models," Mathematics, MDPI, vol. 11(4), pages 1-14, February.

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