摘要：In many applications, the number of the important predictors or features may exceeds the sample size. To address the problem, combining the square root lasso and the structured fused lasso, we propose a new regularization and variable selection technique called the weighted structured square-root fused lasso for high-dimensional linear regression models, in which the regression coefficients are unnecessarily too sparse but the specific structures of which are sparse. A key feature of the proposed method is that the reasonable regularization parameters are independent of the unknown noise level. We establish some nonasymptotic error bounds of the estimation and the prediction, and show that the proposed method can identify the signs of the structured regression coefficients correctly with very high probability, under some mild conditions. By means of the ADMM (alternating direction method of multipliers) algorithm, we provide a computational approach to obtain the estimator. Simulated examples with different structure of the true regression coefficients demonstrate the remarkable performance of the proposed method in estimation, variable selection, and prediction. We finally apply the proposed method to a dataset of expression quantitative trait locus.

报告人简介：厦门大学数学科学学院教授、博士生导师，兼任中国现场统计研究会理事、中国现场统计研究会高维数据统计分会理事。主要从事潜在变量模型、非/半参数统计模型及时间序列分析的研究工作。主持完成国家和福建省自然科学基金面上项目多项。多次应邀赴香港中文大学统计系进行合作研究。已在British Journal of Mathematical and Statistical Psychology、Computational Statistics and Data Analysis、Journal of Applied Probability、Journal of Time Series Analysis、Journal of Nonparametric Statistics、Psychometrika、Science China: Mathematics、Statistics and Computing等国内外数学、概率、统计、心理学等主流学术期刊上发表了系列的学术论文。