Mean Squared Error MSE of Estimators, and Alternatives

In statistical literature, it is common to quantify the performance of an estimator nsing mean squared error (MSE). MSE is the average squared deviation of estimates 

Application of Uncertainty Analysis to Ecological Risk of Pesticides 

One often encounters a distinction between precision and accuracy. Accuracy relates to systematic deviation between parameter estimates and actual parameter values precision relates to the spread in the distribution of estimates. This terminology is not often used explicitly in the estimation theory literature, but the concepts are often implicit. 

MSE reflects a combination of the accuracy and precision of an estimator. A convenient feature is that MSE can be decomposed into parts that correspond to accuracy and precision. 

In general, bias refers to a tendency for parameter estimates to deviate systematically from the true parameter value, based on some measure of the central tendency of the sampling distribution. In other words, bias is imperfect accuracy. In statistics, what is most often meant is mean-unbiasedness. In this sense, an estimator is unbiased (UB) if the average value of estimates (averaging over the sampling distribution) is equal to the true value of the parameter. For example, the mean value of the sample mean (over the sampling distribution of the sample mean) equals the mean for the population. This chapter adheres to the statistical convention of using the term bias (without qualification) to mean mean-unbiasedness. 

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