Confidence Intervals for Model Parameters
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This chapter studies the problem of construction of confidence intervals for 1-parameter models. It uses the special case of the Gaussian distribution to introduce the notions of pivot and approximate pivot. Then, the determination of more general approximate pivots is discussed in the context of exponential families, by means of Wald’s method and likelihood ratios. The duality with hypothesis tests is then introduced, and used to show how optimal one-sided tests can yield optimal one-sided intervals in exponential families.