论文标题
基于图形的线性模型的自适应估计和统计推断
Adaptive Estimation and Statistical Inference for High-Dimensional Graph-Based Linear Models
论文作者
论文摘要
我们考虑基于图形的线性模型的自适应估计和统计推断。在我们的模型中，回归系数的坐标对应于潜在的无向图。此外，给定的图控制回归载体的分段多项式结构。在自适应估计部分中，我们采用基于图的正则化技术，并提出了一个局部自适应估计剂家族，称为图形 - picewise-polynomial-lasso。我们进一步研究了用于统计推断问题的图形 - 聚集体 - lasso的一步更新。我们开发了相应的理论，其中包括固定设计和次高斯随机设计。最后，我们通过广泛的仿真研究说明了方法的出色表现，并以拟南芥微阵列数据集的应用程序结论。
We consider adaptive estimation and statistical inference for high-dimensional graph-based linear models. In our model, the coordinates of regression coefficients correspond to an underlying undirected graph. Furthermore, the given graph governs the piecewise polynomial structure of the regression vector. In the adaptive estimation part, we apply graph-based regularization techniques and propose a family of locally adaptive estimators called the Graph-Piecewise-Polynomial-Lasso. We further study a one-step update of the Graph-Piecewise-Polynomial-Lasso for the problem of statistical inference. We develop the corresponding theory, which includes the fixed design and the sub-Gaussian random design. Finally, we illustrate the superior performance of our approaches by extensive simulation studies and conclude with an application to an Arabidopsis thaliana microarray dataset.
