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首页> 外文期刊>Scandinavian journal of statistics >Simultaneous Confidence Bands for Linear Regression with Covariates Constrained in Intervals
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Simultaneous Confidence Bands for Linear Regression with Covariates Constrained in Intervals

机译：间隔受协变量约束的线性回归的同时置信带

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摘要

The focus of this article is on simultaneous confidence bands over a rectangular covariate region for a linear regression model with k>1 covariates, for which only conservative or approximate confidence bands are available in the statistical literature stretching back to Working & Hotelling (J. Amer. Statist. Assoc. 24, 1929; 73-85). Formulas of simultaneous confidence levels of the hyperbolic and constant width bands are provided. These involve only a k-dimensional integral; it is unlikely that the simultaneous confidence levels can be expressed as an integral of less than k-dimension. These formulas allow the construction for the first time of exact hyperbolic and constant width confidence bands for at least a small k(>1) by using numerical quadrature. Comparison between the hyperbolic and constant width bands is then addressed under both the average width and minimum volume confidence set criteria. It is observed that the constant width band can be drastically less efficient than the hyperbolic band when k > 1. Finally it is pointed out how the methods given in this article can be applied to more general regression models such as fixed-effect or random-effect generalized linear regression models.
机译：本文的重点是在k> 1协变量的线性回归模型的矩形协变量区域上的同时置信带，在统计文献中只有保守或近似的置信带才可以追溯到Working＆Hotelling（J.Amer （Statist。Assoc.24，1929； 73-85）。提供了双曲和恒定宽度带的同时置信度的公式。这些仅涉及k维积分；同时置信度水平不可能表示为小于k维的整数。这些公式允许使用数值正交首次构造至少为小k（> 1）的精确双曲和恒定宽度置信带。然后在平均宽度和最小体积置信度设置标准下都解决了双曲和恒定宽度带之间的比较。可以看出，当k> 1时，恒定宽度带的效率可能大大低于双曲带。最后指出了本文中给出的方法如何可应用于更通用的回归模型，例如固定效应或随机变量。影响广义线性回归模型。

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