Definition
Suppose there is a fixed parameter that needs to be estimated. Then an "estimator" is a function that maps the sample space to a set of sample estimates. An estimator of is usually denoted by the symbol . It is often convenient to express the theory using the algebra of random variables: thus if X is used to denote a random variable corresponding to the observed data, the estimator (itself treated as a random variable) is symbolised as a function of that random variable, . The estimate for a particular observed dataset (i.e. for X=x) is then, which is a fixed value. Often an abbreviated notation is used in which is interpreted directly as a random variable, but this can cause confusion.
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