This paper provides the method of constructing the simultaneous confidence band for a percentile hyper-plane with predictor variables constrained in an ellipsoidal region. The band is compared with that on a rectangular region. It is shown that the band on the ellipsoidal region has a big advantage. The proposed method allows to construct the Type I band and the Type II band, and also allows to constrain the predictor variables either in finite intervals or in infinite intervals. In order to evaluate the efficiency of the band, the average width criterion is introduced, under which the Type I band and the Type II band are compared. All stated above are illustrated by a real example of a leaching rate study.

中文翻译：

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预测变量约束在椭球区域内的百分位超平面的同时置信带的构建

本文提供了为预测变量约束在椭圆体区域内的百分位超平面构建同时置信带的方法。该带与矩形区域上的带进行比较。结果表明，椭圆区域上的能带具有很大的优势。所提出的方法允许构建类型 I 波段和类型 II 波段，并且还允许在有限间隔或无限间隔中约束预测变量。为了评估频段的效率，引入了平均宽度标准，在该标准下比较了Type I频段和Type II频段。上述所有内容均通过浸出率研究的真实示例进行说明。