When confronted with multiple covariates and a response variable, analysts sometimes apply a variable‐selection algorithm to the covariate‐response data to identify a subset of covariates potentially associated with the response, and then wish to make inferences about parameters in a model for the marginal association between the selected covariates and the response. If an independent data set were available, the parameters of interest could be estimated by using standard inference methods to fit the postulated marginal model to the independent data set. However, when applied to the same data set used by the variable selector, standard (“naive”) methods can lead to distorted inferences. The authors develop testing and interval estimation methods for parameters reflecting the marginal association between the selected covariates and response variable, based on the same data set used for variable selection. They provide theoretical justification for the proposed methods, present results to guide their implementation, and use simulations to assess and compare their performance to a sample‐splitting approach. The methods are illustrated with data from a recent AIDS study. The Canadian Journal of Statistics 37: 625–644; 2009 © 2009 Statistical Society of Canada

中文翻译：

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使用受限排列方法进行变量选择后的推断。

当面对多个协变量和一个响应变量时，分析人员有时将变量选择算法应用于协变量响应数据，以识别可能与响应相关的协变量子集，然后希望对模型中的参数进行推断以获取边际所选协变量与响应之间的关联。如果独立数据集可用，则可以通过使用标准推理方法将假设的边际模型拟合到独立数据集来估计感兴趣的参数。但是，当应用于变量选择器使用的相同数据集时，标准（“天真”）方法可能会导致推断失真。基于用于变量选择的相同数据集，作者为反映所选协变量和响应变量之间的边际关联的参数开发了测试和区间估计方法。他们为所提出的方法提供了理论依据，展示了指导其实施的结果，并使用模拟来评估和比较其性能与样本分割方法。这些方法用最近一项艾滋病研究的数据进行了说明。加拿大统计杂志 37：625-644；2009 © 2009 加拿大统计学会 这些方法用最近一项艾滋病研究的数据进行了说明。加拿大统计杂志 37：625-644；2009 © 2009 加拿大统计学会 这些方法用最近一项艾滋病研究的数据进行了说明。加拿大统计杂志 37：625-644；2009 © 2009 加拿大统计学会