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<p>In this paper, we consider estimation and statistical inference for a mixed matrix-vector linear regression model by relaxing the independency entries restriction to a general Kronecker structure. A two-step estimation approach based on decorrelated score and rotation is proposed without additional debiasing procedure. In the first step, to deal with the high-dimensional nuisance matrix estimator, we construct an unbiased estimator for the vector parameter based on the decorrelated score function. In the second step, to achieve an unbiased and asymptotically normality estimator for the matrix estimator, we employ the sample-splitting and rotation-unbiasedness techniques. The Cramér-Rao lower bound of the proposed estimator for any linear function of matrix coefficient is attained. Simulation studies and an empirical analysis of Beijing air quality dataset demonstrate the superior performance of our proposed estimators.</p>

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Statistical inference for matrix-vector linear regression without debiasing under Kronecker covariance structure

  • 期刊论文

  • 发表日期：

    2025年9月24日

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  • Baofang Ke,
  • Weihua Zhao,
  • Lei Wang

摘要

In this paper, we consider estimation and statistical inference for a mixed matrix-vector linear regression model by relaxing the independency entries restriction to a general Kronecker structure. A two-step estimation approach based on decorrelated score and rotation is proposed without additional debiasing procedure. In the first step, to deal with the high-dimensional nuisance matrix estimator, we construct an unbiased estimator for the vector parameter based on the decorrelated score function. In the second step, to achieve an unbiased and asymptotically normality estimator for the matrix estimator, we employ the sample-splitting and rotation-unbiasedness techniques. The Cramér-Rao lower bound of the proposed estimator for any linear function of matrix coefficient is attained. Simulation studies and an empirical analysis of Beijing air quality dataset demonstrate the superior performance of our proposed estimators.