数学与统计学院知识库

模型选择后的统计推断问题是近年来统计领域的热点课题之一. 传统的统计分析首先进行模型选择, 然后对后模型参数直接进行统计推断. 近年来, 一些学者指出, 如果不考虑模型选择对统计推断的影响, 通常会造成推断结果偏差较大的问题. 为了克服这一问题, 他们提出了模型选择后推断(post-selection inference, PSI) 方法对此问题予以修正.
在本论文中, 我们研究了自回归模型的选择后推断问题. 首先, 基于时间序列模型的lasso 选择理论, 我们探讨了自回归模型的参数选择问题. 其次, 针对已经选中的模型参数, 我们建立了模型中参数的选择后推断, 证明了相应的渐近性质.同时, 我们进行了大量的模拟研究, 实验结果表明, 相较于传统的统计推断方法,模型选择后推断方法不仅能够得到较为准确的点估计, 而且参数的置信区间和P值等均表现优异. 最后, 我们将此方法应用在实际数据分析中, 通过对比模型选择后推断方法和传统"Box-Jenkins"方法的预测能力, 我们发现模型选择后推断方法能够得到较为准确和稳健的预测结果.

Post selection inference is one of the hot topic in statistics and statistical machine learning. In the classical inference theory, data are assumed to generate from a know model, and we use model selection to obtain the candidate (sub)model. Generally, we often ignore the e ects of model selection, just to make inference about the properties of the parameters in the model of interest. Recently, however, the problem of inference after model selection has been recognized by some researchers, and they propose post-selection inference(PSI) methods to solve this problems.

In this thesis, we propose the methods about post-selection inference for autoregressive models. Firstly, we study the theoretical properties of lasso estimate in sparse autoregressive models by utilizing the spectral properties of stationary processes. Secondly, we consider to get the valid meaningful inference after model selection under selective inference framework. Our simulation studies show that not only point estimation and con dence intervals, but the null coefficients P-values are better than classical "Box-Jenkins" method. Finally, we apply our method to real data, and test the prediction performance, the results show that post-selection inference has more accurate and robust performance than classical methods.