Inference for bounded parameters

Details Inference for bounded parameters Inference for bounded parameters

2003-03-27

arxiv.org/abs/physics/0303111v2

Physics

Data Analysis, Statistics and Probability

Scientific paper

10.1103/PhysRevD.69.033002

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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