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  • Articles  (2)
  • Biometrika  (2)
  • 3549
  • Mathematics  (2)
  • 1
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    Oxford University Press
    Publication Date: 2015-08-21
    Description: Sufficient dimension reduction in regression aims to reduce the predictor dimension by replacing the original predictors with some set of linear combinations of them without loss of information. Numerous dimension reduction methods have been developed based on this paradigm. However, little effort has been devoted to diagnostic studies within the context of dimension reduction. In this paper we introduce methods to check goodness-of-fit for a given dimension reduction subspace. The key idea is to extend the so-called distance correlation to measure the conditional dependence relationship between the covariates and the response given a reduction subspace. Our methods require minimal assumptions, which are usually much less restrictive than the conditions needed to justify the original methods. Asymptotic properties of the test statistic are studied. Numerical examples demonstrate the effectiveness of the proposed approach.
    Print ISSN: 0006-3444
    Electronic ISSN: 1464-3510
    Topics: Biology , Mathematics , Medicine
    Location Call Number Limitation Availability
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  • 2
    Publication Date: 2016-09-04
    Description: The envelope model allows efficient estimation in multivariate linear regression. In this paper, we propose the sparse envelope model, which is motivated by applications where some response variables are invariant with respect to changes of the predictors and have zero regression coefficients. The envelope estimator is consistent but not sparse, and in many situations it is important to identify the response variables for which the regression coefficients are zero. The sparse envelope model performs variable selection on the responses and preserves the efficiency gains offered by the envelope model. Response variable selection arises naturally in many applications, but has not been studied as thoroughly as predictor variable selection. In this paper, we discuss response variable selection in both the standard multivariate linear regression and the envelope contexts. In response variable selection, even if a response has zero coefficients, it should still be retained to improve the estimation efficiency of the nonzero coefficients. This is different from the practice in predictor variable selection. We establish consistency and the oracle property and obtain the asymptotic distribution of the sparse envelope estimator.
    Print ISSN: 0006-3444
    Electronic ISSN: 1464-3510
    Topics: Biology , Mathematics , Medicine
    Location Call Number Limitation Availability
    BibTip Others were also interested in ...
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