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Bootstrapping for multivariate linear regression models

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  • Eck, Daniel J.

Abstract

The multivariate linear regression model is an important tool for investigating relationships between several response variables and several predictor variables. The primary interest is in inference about the unknown regression coefficient matrix. We propose multivariate bootstrap techniques as a means for making inferences about the unknown regression coefficient matrix. These bootstrapping techniques are extensions of those developed in Freedman (1981), which are only appropriate for univariate responses. Extensions to the multivariate linear regression model are made without proof. We formalize this extension and prove its validity. A real data example and two simulated data examples which offer some finite sample verification of our theoretical results are provided.

Suggested Citation

  • Eck, Daniel J., 2018. "Bootstrapping for multivariate linear regression models," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 141-149.
    • Handle: RePEc:eee:stapro:v:134:y:2018:i:c:p:141-149
    DOI: 10.1016/j.spl.2017.11.001
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    1. Lai, T. L. & Robbins, Herbert & Wei, C. Z., 1979. "Strong consistency of least squares estimates in multiple regression II," Journal of Multivariate Analysis, Elsevier, vol. 9(3), pages 343-361, September.
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