Customary confidence regions do not truly reflect in the majority of our geodetic applications the confidence one can have in one’s produced estimators. As it is common practice in our daily data analyses to combine methods of parameter estimation and hypothesis testing before the final estimator is produced, it is their combined uncertainty that has to be taken into account when constructing confidence regions. Ignoring the impact of testing on estimation will produce faulty confidence regions and therefore provide an incorrect description of estimator’s quality. In this contribution, we address the interplay between estimation and testing and show how their combined non-normal distribution can be used to construct truthful confidence regions. In doing so, our focus is on the designing phase prior to when the actual measurements are collected, where it is assumed that the working (null) hypothesis is true. We discuss two different approaches for constructing confidence regions: Approach I in which the region’s shape is user-fixed and only its size is determined by the distribution, and Approach II in which both the size and shape are simultaneously determined by the estimator’s non-normal distribution. We also prove and demonstrate that the estimation-only confidence regions have a poor coverage in the sense that they provide an optimistic picture. Next to the provided theory, we provide computational procedures, for both Approach I and Approach II, on how to compute confidence regions and confidence levels that truthfully reflect the combined uncertainty of estimation and testing.

在我们的大多数大地测量应用程序中，习惯置信区域并不能真正反映人们对自己产生的估计器的置信度。由于我们日常数据分析中的常见做法是在生成最终估计量之前结合参数估计和假设检验的方法，因此在构建置信区域时必须考虑它们的组合不确定性。忽略测试对估计的影响会产生错误的置信区域，因此会提供对估计器质量的错误描述。在这篇文章中，我们解决了估计和测试之间的相互作用，并展示了如何使用它们的组合非正态分布来构建真实的置信区域。这样做时，我们的重点是收集实际测量值之前的设计阶段，假设工作（零）假设为真。我们讨论了构建置信区域的两种不同方法：方法一，其中区域的形状是用户固定的，只有它的大小由分布决定，方法二，大小和形状同时由估计器的非正态分布决定。我们还证明并证明了仅估计置信区域的覆盖范围很差，因为它们提供了乐观的图片。除了所提供的理论之外，我们还为方法 I 和方法 II 提供了计算程序，说明如何计算真实反映估计和测试的组合不确定性的置信区域和置信水平。