Elements of Parameter Estimation
In Chapters II and III we have considered the design of optimum procedures for deciding between two possible statistical situations on the basis of a random observation Y. In many situations arising in practice we are interested not in making a choice between two (or among several) discrete situations, but rather in making a choice among a continuum of possible states of nature. In particular, as in the composite hypothesis-testing problems discussed in Chapter II, we can think of a family of distributions on the observation space, indexed by a parameter or set of parameters. But unlike the case of composite hypothesis testing in which we wish to make a binary decision about the parameter, we wish here to determine as accurately as possible the actual value of the parameter from the observation.
KeywordsUnbiased Estimator Exponential Family Likelihood Equation Bayesian Parameter Estimation Information Inequality
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