## Various Measures of Closeness

The ambiguity of the first kind is resolved once we decide on a measure of closeness between the estimator and the parameter. There are many reasonable measures of closeness, however, and it is not easy to choose a particular one. In this section we shall consider six measures of closeness and establish relationships among them. In the following discussion we shall denote two competing estimators by X and F and the parameter by 0. Note that 0 is always a fixed number in the present analysis. Each of the six statements below gives the condition under which estimator X is preferred to estimator Y. (We allow for the possibility of a tie. If X is preferred to Y and Y is not preferred to X, we say X is strictly preferred to F.) Or, we might say, X is “better” than F...

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