Inference for bounded parameters

Abstract

The estimation of signal frequency count in the presence of background noise has had much discussion in the recent physics literature, and Mandelkern [1] brings the central issues to the statistical community, leading in turn to extensive discussion by statisticians. The primary focus however in [1] and the accompanying discussion is on the construction of a confidence interval. We argue that the likelihood function and $p$-value function provide a comprehensive presentation of the information available from the model and the data. This is illustrated for Gaussian and Poisson models with lower bounds for the mean parameter.

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Cited by in corpus (3)

• Is Bayes Posterior just Quick and Dirty Confidence?
• Measurement of the top quark pair production cross section in proton-proton collisions at sqrt(s) = 13 TeV
• The Banff Challenge: Statistical Detection of a Noisy Signal