A Minimum variance approach to multivariate linear regression with application to actuarial problems

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      <subfield code="a">A Minimum variance approach to multivariate linear regression with application to actuarial problems</subfield>
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      <subfield code="a">Variability is inherent in statistical, actuarial, and economic models, necessitating precise quantification for informed decision-making and risk management. Recently, Landsman and Shushi introduced the Location of Minimum Variance Squared Distance (LVS) risk functional, a novel variance-based measure of variability. We extend LVS to assess variability in regression models commonly used in actuarial analysis, enabling the construction of regression-type predictors in the Minimum Variance Squared Deviation (MVS) sense. We show that when the predicted vector Y follows a symmetric distribution, MVS aligns with the traditional Minimum Expected Squared Deviation (MES) functional. However, for non-symmetric distributions, MVS and MES diverge, with differences influenced by the joint third-moment matrix of distribution P and the covariance matrix of Y. We derive an analytical expression for MVS and explore a hybrid approach combining MVS and MES functionals. To illustrate the applicability of our approach, we present two numerical examples: (i) predicting three components of fire lossesbuildings, contents, and profitsand (ii) forecasting returns for six market indices based on the returns of their dominant stocks</subfield>
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      <subfield code="g">15/12/2025 Volume 15 Issue 3 - December 2025 , 22 p.</subfield>
      <subfield code="t">European Actuarial Journal</subfield>
      <subfield code="d">Cham, Switzerland  : Springer Nature Switzerland AG,  2021-2022</subfield>
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