论文标题
线性回归中设置的级别设置
Confidence Sets for a level set in linear regression
论文作者
论文摘要
回归建模是统计的主力，并且关于回归函数的估计有大量文献。近年来，在回归分析中，最终目标可能是对回归函数的水平集的估计，而不是回归函数本身的估计。迄今为止，有关估计集合估计的已发表的工作主要集中在非参数回归上，尤其是在点估计上。在本文中，考虑了线性回归水平集的置信度集合。特别是，为正常误差线性回归构建了$ 1-α$级别的上，下，下部和双面置信度集。结果表明，这些置信集可以轻松地从相应的$ 1-α$级别同时置信带中构建。还可以指出，构造方法容易适用于其他参数回归模型，在其他参数回归模型中，通过单调链接函数，平均响应取决于线性预测器，其中包括通用线性模型，线性混合模型和广义线性混合模型。因此，本文提出的方法广泛适用。举例说明了该方法。
Regression modeling is the workhorse of statistics and there is a vast literature on estimation of the regression function. It is realized in recent years that in regression analysis the ultimate aim may be the estimation of a level set of the regression function, instead of the estimation of the regression function itself. The published work on estimation of the level set has thus far focused mainly on nonparametric regression, especially on point estimation. In this paper, the construction of confidence sets for the level set of linear regression is considered. In particular, $1-α$ level upper, lower and two-sided confidence sets are constructed for the normal-error linear regression. It is shown that these confidence sets can be easily constructed from the corresponding $1-α$ level simultaneous confidence bands. It is also pointed out that the construction method is readily applicable to other parametric regression models where the mean response depends on a linear predictor through a monotonic link function, which include generalized linear models, linear mixed models and generalized linear mixed models. Therefore the method proposed in this paper is widely applicable. Examples are given to illustrate the method.
