ABSTRACT

So called multiple correlation coefficient (MCC) is a measure of linear relationship between a given variable and set of covariates. In the multiple correlation and regression analysis, it is common practice to construct a confidence interval for the population MCC. In high-dimensional data settings, by which the data dimension p is much larger than the sample size n, due to the singularity of the sample covariance matrix, the classical confidence intervals for the MCC are no longer useable. For high-dimensional elliptical data, some (conservative) confidence intervals for the population MCC are presented using the random projection methodology. To evaluate and compare the performance of the proposed confidence intervals, some simulations are conducted in terms of the coverage probability and average interval length. Experimental validation of the proposed intervals is carried out on two real gene expression datasets.

摘要

所谓的多重相关系数 (MCC) 是对给定变量和一组协变量之间线性关系的度量。在多元相关和回归分析中，通常的做法是为总体 MCC 构建置信区间。在高维数据设置中，数据维度p远大于样本大小n，由于样本协方差矩阵的奇异性，MCC 的经典置信区间不再可用。对于高维椭圆数据，总体 MCC 的一些（保守）置信区间是使用随机投影方法呈现的。为了评估和比较建议的置信区间的性能，在覆盖概率和平均区间长度方面进行了一些模拟。在两个真实的基因表达数据集上对所提出的区间进行了实验验证。