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Optimal estimation of direction in regression models with large number of parameters

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  • Gillard, Jonathan
  • Zhigljavsky, Anatoly

Abstract

We consider the problem of estimating the optimal direction in regression by maximizing the probability that the scalar product between the vector of unknown parameters and the chosen direction is positive. The estimator maximizing this probability is simple in form, and is especially useful for situations where the number of parameters is much larger than the number of observations. We provide examples which show that this estimator is superior to state-of-the-art methods such as the LASSO for estimating the optimal direction.

Suggested Citation

  • Gillard, Jonathan & Zhigljavsky, Anatoly, 2018. "Optimal estimation of direction in regression models with large number of parameters," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 281-289.
    • Handle: RePEc:eee:apmaco:v:318:y:2018:i:c:p:281-289
    DOI: 10.1016/j.amc.2017.05.050
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    References listed on IDEAS

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    1. Nicolai Meinshausen & Peter Bühlmann, 2010. "Stability selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 417-473, September.
    2. Lolli, Gabriele, 2015. "Metamathematical investigations on the theory of Grossone," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 3-14.
    3. Rajen D. Shah & Richard J. Samworth, 2013. "Variable selection with error control: another look at stability selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(1), pages 55-80, January.
    4. 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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