Confidence Intervals

Construction of Exact Simultaneous Confidence Bands for a Simple Linear Regression Model



A simultaneous confidence band provides a variety of inferences on the unknown components of a regression model. Construction of simultaneous confidence bands for a simple linear regression model has a rich history, going back to(1929). The purpose of this article is to consolidate the disparate modern literature on simultaneous confidence bands in linear regression, and to provide expressions for the construction of exact 1−αlevel simultaneous confidence bands for a simple linear regression model of either one-sided or two-sided form.We center attention on the three most recognized shapes:hyperbolic, two-segment, and three-segment (which is also referred to as a trapezoidal shape and includes a constant-width band as a special case). Some of these expressions have already appeared in
the statistics literature, and some are newly derived in this article. The derivations typically involve a standard bivariate t random vector and its polar coordinate transformation.

Key words: Simple linear regression; simultaneous inferences; bivariate normal; bivariate t; polar coordinators.

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