A strongly consistent procedure for model selection in a regression problem
A strongly consistent procedure for model selection in a regression problem
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DOI：
10.1093/biomet/76.2.369
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发表时间：
1989-06
期刊：
影响因子：
2.7
通讯作者：
Calyampudi R. Rao;Yuehua Wu
中科院分区：
文献类型：
--
作者：
Calyampudi R. Rao;Yuehua Wu
我们考虑多元回归模型Yn = Xn, + En，其中Yn和En为n向量随机变量，Xn为n x m矩阵，83为未知回归参数的m向量。，3的每个分量可以为零或非零，这就产生了2种可能的多元回归模型。我们提供了一个选择模型的决策规则，该决策规则与真模型强一致为n -> 0。这个结果是在某些温和的条件下证明的，例如，不假设En的分量分布的正态性。
SUMMARY We consider the multiple regression model Yn = Xn, + En, where Yn and En are n-vector random variables, Xn is an n x m matrix and 83 is an m-vector of unknown regression parameters. Each component of ,3 may be zero or nonzero, which gives rise to 2' possible models for multiple regression. We provide a decision rule for the choice of a model which is strongly consistent for the true model as n -> oo. The result is proved under certain mild conditions, for instance without assuming normality of the distribution of the components of En.