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Confidence intervals in regression centred on the SCAD estimator

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  • Farchione, Davide
  • Kabaila, Paul

Abstract

Consider a linear regression model. Fan and Li (2001) describe the smoothly clipped absolute deviation (SCAD) point estimator of the regression parameter vector. To gain insight into the properties of this estimator, they consider an orthonormal design matrix and focus on the estimation of a specified component of this vector. They show that the SCAD point estimator has three attractive properties. We answer the question: to what extent can an interval estimator, centred on the SCAD estimator, have similar attractive properties?

Suggested Citation

  • Farchione, Davide & Kabaila, Paul, 2012. "Confidence intervals in regression centred on the SCAD estimator," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1953-1960.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:11:p:1953-1960
    DOI: 10.1016/j.spl.2012.06.027
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    References listed on IDEAS

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    1. Kabaila, Paul, 2011. "Admissibility of the usual confidence interval for the normal mean," Statistics & Probability Letters, Elsevier, vol. 81(3), pages 352-359, March.
    2. Farchione, David & Kabaila, Paul, 2008. "Confidence intervals for the normal mean utilizing prior information," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1094-1100, July.
    3. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
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    Cited by:

    1. Kabaila, Paul, 2013. "Note on a paradox in decision-theoretic interval estimation," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 123-126.

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