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On the use of comparison regions in visualizing stochastic uncertainty in some two‐parameter estimation problems
Author(s) -
Eckert Maren,
Vach Werner
Publication year - 2020
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201800232
Subject(s) - inference , simple (philosophy) , point estimation , post hoc , regular polygon , parameter space , computer science , statistical inference , visualization , statistical hypothesis testing , point (geometry) , mathematics , null hypothesis , algorithm , statistics , data mining , artificial intelligence , medicine , philosophy , geometry , dentistry , epistemology
When considering simultaneous inference for two parameters, it is very common to visualize stochastic uncertainty by plotting two‐dimensional confidence regions. This allows us to test post hoc null hypotheses about a single point in a simple manner. However, in some applications the interest is not in rejecting hypotheses on single points, but in demonstrating evidence for the two parameters to be in a convex subset of the parameter space. The specific convex subset to be considered may vary from one post hoc analysis to another. Then it is of interest to have a visualization allowing to perform corresponding analyses. We suggest comparison regions as a simple tool for this task.