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Sufficient dimension reduction and prediction in regression: Asymptotic results

Author

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  • Forzani, Liliana
  • Rodriguez, Daniela
  • Smucler, Ezequiel
  • Sued, Mariela

Abstract

We consider model-based sufficient dimension reduction for generalized linear models and prove the consistency and asymptotic normality of the prediction estimator studied empirically for the normal case by Adragni and Cook (2009) when a sample version of the sufficient dimension reduction is used. Moreover, we provide a formula for the prediction that does need require explicitly computing the reduction.

Suggested Citation

  • Forzani, Liliana & Rodriguez, Daniela & Smucler, Ezequiel & Sued, Mariela, 2019. "Sufficient dimension reduction and prediction in regression: Asymptotic results," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 339-349.
    • Handle: RePEc:eee:jmvana:v:171:y:2019:i:c:p:339-349
    DOI: 10.1016/j.jmva.2018.12.003
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    References listed on IDEAS

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    1. Efstathia Bura & Sabrina Duarte & Liliana Forzani, 2016. "Sufficient Reductions in Regressions With Exponential Family Inverse Predictors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1313-1329, July.
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    6. Diego Tomassi & Liliana Forzani & Efstathia Bura & Ruth Pfeiffer, 2017. "Sufficient dimension reduction for censored predictors," Biometrics, The International Biometric Society, vol. 73(1), pages 220-231, March.
    7. R. Dennis Cook & Liliana Forzani, 2008. "Covariance reducing models: An alternative to spectral modelling of covariance matrices," Biometrika, Biometrika Trust, vol. 95(4), pages 799-812.
    8. Cook, R. Dennis & Forzani, Liliana, 2009. "Likelihood-Based Sufficient Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 197-208.
    9. Li, Bing & Wang, Shaoli, 2007. "On Directional Regression for Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 997-1008, September.
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