[Statlist] Next talk: Friday, 16.11.2018, with Zijian Guo Rutgers, The State University of New Jersey

[Maurer Letizia]

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ETH and University of Zurich

Organisers:

Proff. P. Bühlmann - L. Held - T. Hothorn - M. Maathuis -
N. Meinshausen - S. van de Geer - M. Wolf

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We are glad to announce the following talk:

Friday, 16.11.2018, at 15.15 h  ETH Zurich HG G19.1
with Zijian Guo, Rutgers, The State University of New Jersey

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Title:

Semi-supervised Inference for Explained Variance in High-dimensional Linear Regression and Its Applications


Abstract:

We consider statistical inference for the explained variance $\beta^{\intercal}\Sigma \beta$ under the  high-dimensional linear model $Y=X\beta+\epsilon$ in the semi-supervised setting, where $\beta$ is the regression vector and $\Sigma$ is the design covariance matrix. A calibrated estimator, which efficiently integrates both labelled and unlabelled data, is proposed. It is shown that the estimator achieves the minimax optimal  rate of convergence in the general semi-supervised framework. The optimality result characterizes how the unlabelled data affects the minimax optimal rate. Moreover,  the limiting distribution for the proposed estimator is established and data-driven confidence intervals for the explained variance are constructed. We further develop a randomized calibration technique for statistical inference in the presence of weak signals and apply the obtained inference results to a range of important statistical problems, including signal detection and global testing, prediction accuracy evaluation, and confidence ball construction. The numerical performance of the proposed methodology is demonstrated in simulation studies and an analysis of estimating heritability for a yeast segregant data set with multiple traits.

This abstract is also to be found under the following link: http://stat.ethz.ch/events/research_seminar

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