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Optimal directional statistic for general regression

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  • Gillard, Jonathan
  • Zhigljavsky, Anatoly

Abstract

For a general linear regression model we construct a directional statistic which maximizes the probability that the scalar product between the vector of unknown parameters and any linear estimator is positive. Special emphasis is given to comparison of this directional statistic with the BLUE and explaining why the BLUE could be relatively poor. We illustrate our results on analytical and numerical examples.

Suggested Citation

  • Gillard, Jonathan & Zhigljavsky, Anatoly, 2018. "Optimal directional statistic for general regression," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 74-80.
    • Handle: RePEc:eee:stapro:v:143:y:2018:i:c:p:74-80
    DOI: 10.1016/j.spl.2018.07.025
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    References listed on IDEAS

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    1. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
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