多元正态预测的二元响应回归模型中的变量筛选
Variable Screenings in Binary Response Regressions with Multivariate Normal Predictors
摘要：
在模型建立之前进行筛选是一种合理的降维策略。当然，独立筛选是达到这一目的的有效方法。它应用简单线性回归的斜率估计值作为响应与预测因子之间关联的替代度量，以便最终模型可以由具有陡峭斜率的预测因子构建。但是，如果响应确实受到某些预测变量的非平凡线性组合的影响，则简单线性回归模型是错误指定的模型。在这项工作中，我们研究了一定的独立性筛选的性能，在模型误设定的二元响应回归。假设预测变量服从多元正态分布，且真实和工作链接函数属于一类正态分布的尺度混合，研究了极大似然筛选和最小二乘筛选。
英文摘要：
Screening before model building is a reasonable strategy to reduce the dimension of regression problems. Sure independence screening is an efficient approach to this purpose. It applies the slope estimate of a simple linear regression as a surrogate measure of the association between the response and the predictor so that the final model can be built by those predictors with steep slopes. However, if the response is truly affected by a nontrivial linear combination of some predictors then the simple linear regression model is a misspecified model. In this work, we investigate the performance of the sure independence screening in the view of model misspecification for binary response regressions. Both maximum likelihood screening and least square screening are studied with the assumption that predictors follow multivariate normal distribution and the true and the working link function belong to a class of scale mixtures of normal distributions.
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