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随着科技的进步,高维数据的产生、收集变得越来越容易;传统的建模方法对变量间的结构处理较为简单,这对高维数据的分析有很大的局限性。高斯图模型可以很好的描述这种结构关系,它将变量间的结构信息通过精度矩阵(协方差矩阵的逆矩阵)中的元素来表示。本文采用CLIME方法估计精度矩阵,并且详细给出CLIME估计下的精度矩阵与其估计量在最大范数下的收敛速度的证明过程,最后将得到的精度矩阵估计量应用于股票价格上,使得股票价格之间的结构关系直观明了。
With the advancement of science and technology, the generation and collection of high-dimensional data become more and more easy. The traditional modeling methods are simpler to deal with the structural changes among variables, which has great limitations on the analysis of high-dimensional data. The Gaussian graph model can describe this kind of structural relationship very well, and it shows the structural information among variables through the elements in the precision matrix (the inverse matrix of the covariance matrix). In this paper, the CLIME method is used to estimate the accuracy matrix, and the proof process of the accuracy matrix under the CLIME estimation and the convergence speed of the estimator under the maximum norm is given in detail. Finally, the estimated accuracy matrix estimator is applied to the stock price, The structure of the relationship between the intuitive and clear.