Search

Large-scale multivariate regression is a fundamental statistical tool with a wide range of applications. This study considers the problem of simultaneously testing a large number of general linear hypotheses, encompassing covariate-effect analysis, analysis of variance, and model comparisons. The challenge that accompanies a large number of tests is the ubiquitous presence of heavy-tailed and/or highly skewed measurement noise, which is the main reason for the failure of conventional least squares-based methods. For large-scale multivariate regression, we develop a set of robust inference methods to explore data features such as heavy tailedness and skewness, which are not visible to least squares methods. The new testing procedure is based on the data-adaptive Huber regression and a new covariance estimator of regression estimates. Under mild conditions, we show that our methods produce consistent estimates of the false discovery proportion. Extensive numerical experiments and an empirical study on quantitative linguistics demonstrate the advantage of the proposed method over many state-of-the-art methods when the data are generated from heavy-tailed and/or skewed distributions. [ABSTRACT FROM AUTHOR]

Aims To evaluate the associations between retinal blood flow (RBF) and optical coherence tomography (OCT) structural measurements in normal-tension glaucoma (NTG) eyes with single-hemifield visual field (VF) damage by the Doppler OCT. Methods The Doppler OCT was used to measure temporal artery (TA) RBF and temporal vein (TV) RBF. Retinal nerve fibre layer thickness (RNFLT) was measured by spectral-domain OCT. Results Forty-three consecutive eyes of 43 patients with NTG with VF defect confined to a single hemifield and 24 eyes of 24 age-matched healthy subjects were studied. TA and TV RBF and RNFLT were reduced in the damaged hemisphere compared with the normal hemisphere (mean (SD), 3.61 (1.68) vs 5.86 (2.59) ÎL/min, p<0.001; 5.61 (2.51) vs 6.94 (2.83) ÎL/min, p=0.010; 69.0 (19.7) vs 99.7 (22.8) Îm, p<0.001). Those values in the normal hemisphere of NTG eyes also decreased compared with the healthy hemisphere of the healthy eyes (8.40 (3.36) ÎL/min, p<0.001; 9.28 (4.47) ÎL/min, p<0.002; 122.8 (20.2) Îm, p<0.001). Multivariate model showed that normal and damaged hemispheres and RNFLT were associated with RBF reduction. In addition, the RBF in the normal hemisphere was lower than that in the healthy hemisphere even after adjusting for RNFLT. Conclusion In NTG eyes with single-hemifield damage, the RBF was significantly reduced in the damaged hemisphere compared with the normal one. The RBF decreased in the normal and damaged hemispheres of NTG eyes compared with the healthy hemisphere independent from RNFLT. [ABSTRACT FROM AUTHOR]