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Large-Scale Inference by Bradley Efron

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Appendix A

Exponential Families

Exponential families are the main connecting idea of classical statistics. Here we will provide a very brief sketch of the theory as it applies to the previous material, particularly that in Chapter 5. Advanced texts such as Lehmann and Romano (2005b) discuss exponential families, and their applications to testing and estimation, in more detail.

A one-parameter exponential family images is a family of probability densities on a subset images of the real line,

where η is the natural or canonical parameter, x is the sufficient ...

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