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Asymptotic properties on high-dimensional multivariate regression M-estimation

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  • Ding, Hao
  • Qin, Shanshan
  • Wu, Yuehua
  • Wu, Yaohua

Abstract

In this paper, we work on a general multivariate regression model under the regime that both p, the number of covariates, and n, the number of observations, are large with p∕n→κ(0<κ<∞). Unlike previous works that focus on a sparse regression vector β, we consider a more interesting situation in which β is composed of two groups: components in group I are large while components in group II are small but possibly not zeros. This study aims to explore the asymptotic behavior of the ridge-regularized high-dimensional multivariate M-estimator of β in group II. By applying the double leave-one-out method, we successfully derive a nonlinear system comprised of two deterministic equations, which characterizes the risk behavior of the M-estimator. The system solution also enables us to yield asymptotic normality for each component of the M-estimator. Moreover, we present rigorous proofs to these approximations that play a critical role in deriving the system. Finally, we perform experimental validations to demonstrate the performance of the proposed system.

Suggested Citation

  • Ding, Hao & Qin, Shanshan & Wu, Yuehua & Wu, Yaohua, 2021. "Asymptotic properties on high-dimensional multivariate regression M-estimation," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:jmvana:v:183:y:2021:i:c:s0047259x21000087
    DOI: 10.1016/j.jmva.2021.104730
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    References listed on IDEAS

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