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英文文献：Oracle Inequalities for High Dimensional Vector Autoregressions-高维向量自回归的Oracle不等式
英文文献作者：Anders Bredahl Kock,Laurent A.F. Callot
英文文献摘要：
This paper establishes non-asymptotic oracle inequalities for the prediction error and estimation accuracy of the LASSO in stationary vector autoregressive models. These inequalities are used to establish consistency of the LASSO even when the number of parameters is of a much larger order of magnitude than the sample size. Furthermore, it is shown that under suitable conditions the number of variables selected is of the right order of magnitude and that no relevant variables are excluded. Next, non-asymptotic probabilities are given for the Adaptive LASSO to select the correct sign pattern (and hence the correct sparsity pattern). Finally conditions under which the Adaptive LASSO reveals the correct sign pattern with probability tending to one are given. Again, the number of parameters may be much larger than the sample size. Some maximal inequalities for vector autoregressions which might be of independent interest are contained in the appendix.
本文建立了稳定向量自回归模型中套索的预测误差和估计精度的非渐近oracle不等式。这些不等式被用来建立套索的一致性，即使参数的数目比样本大小大得多。在适当的条件下，所选取的变量的数量级是正确的，不排除任何相关的变量。接下来，给出了自适应套索选择正确符号模式(因此是正确的稀疏模式)的非渐近概率。最后给出了自适应套索在概率趋于1的情况下揭示正确符号模式的条件。同样，参数的数量可能比样本容量大得多。一些向量自回归的极大不等式可能是独立的兴趣包含在附录中。
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