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• W2808068360 abstract "We consider statistical inference for the explained variance $beta^{intercal}Sigma beta$ under the high-dimensional linear model $Y=Xbeta+epsilon$ 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." @default.
• W2808068360 created "2018-06-21" @default.
• W2808068360 creator A5044611660 @default.
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• W2808068360 date "2018-06-16" @default.
• W2808068360 modified "2023-10-18" @default.
• W2808068360 title "Semi-supervised Inference for Explained Variance in High-dimensional Linear Regression and Its Applications" @default.
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