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Principal Hessian Directions for regression with measurement error

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  • Heng-Hui Lue

Abstract

We consider a nonlinear regression problem with predictors with measurement error. We assume that the response is related to unknown linear combinations of a p-dimensional predictor vector through an unknown link function. Instead of observing the predictors, we observe a surrogate vector with the property that its expectation is linearly related to the predictor vector with constant variance. We use an important linear transformation of the surrogates. Based on the transformed variables, we develop the modified Principal Hessian Directions method for estimating the subspace of the effective dimension-reduction space. We derive the asymptotic variances of the modified Principal Hessian Directions estimators. Several examples are reported and comparisons are made with the sliced inverse regression method of Carroll & Li (1992). Copyright Biometrika Trust 2004, Oxford University Press.

Suggested Citation

  • Heng-Hui Lue, 2004. "Principal Hessian Directions for regression with measurement error," Biometrika, Biometrika Trust, vol. 91(2), pages 409-423, June.
  • Handle: RePEc:oup:biomet:v:91:y:2004:i:2:p:409-423
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    Cited by:

    1. Heng-Hui Lue, 2015. "An Inverse-regression Method of Dependent Variable Transformation for Dimension Reduction with Non-linear Confounding," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 760-774, September.
    2. Zhang, Jun & Zhu, Li-Ping & Zhu, Li-Xing, 2012. "On a dimension reduction regression with covariate adjustment," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 39-55, February.
    3. Eliana Christou, 2020. "Robust dimension reduction using sliced inverse median regression," Statistical Papers, Springer, vol. 61(5), pages 1799-1818, October.

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