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High-dimensional variable screening and bias in subsequent inference, with an empirical comparison

Bühlmann, Peter ; Mandozzi, Jacopo

In: Computational Statistics, 2014, vol. 29, no. 3-4, p. 407-430

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    Titre
    • High-dimensional variable screening and bias in subsequent inference, with an empirical comparison
    Auteur
    • Bühlmann, Peter. Seminar for Statistics, ETH, Zurich, Switzerland
    • Mandozzi, Jacopo. Seminar for Statistics, ETH, Zurich, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Computational Statistics, 2014, vol. 29, no. 3-4, p. 407-430. Springer Berlin Heidelberg
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:325774
    Summary
    We review variable selection and variable screening in high-dimensional linear models. Thereby, a major focus is an empirical comparison of various estimation methods with respect to true and false positive selection rates based on 128 different sparse scenarios from semi-real data (real data covariables but synthetic regression coefficients and noise). Furthermore, we present some theoretical bounds for the bias in subsequent least squares estimation, using the selected variables from the first stage, which have direct implications for construction of p-values for regression coefficients.