Editing Estimator (section)

==Definition==
Suppose a fixed ''parameter'' <math>\theta</math> needs to be estimated. Then an "estimator" is a function that maps the [[sample space]] to a set of ''sample estimates''. An estimator of <math>\theta</math> is usually denoted by the symbol <math>\widehat{\theta}</math>. 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, <math>\widehat{\theta}(X)</math>. The estimate for a particular observed data value <math>x</math> (i.e. for <math>X=x</math>) is then  <math>\widehat{\theta}(x)</math>, which is a fixed value. Often an abbreviated notation is used in which <math>\widehat{\theta}</math> is interpreted directly as a [[random variable]], but this can cause confusion.