Frequentist Criteria for Evaluating Estimators, the Sampling Distribution

1 Frequentist Criteria for Evaluating Estimators, the Sampling Distribution 

In classical statistics, the most important type of criterion for judging estimators is a high probability that a parameter estimate will be close to the actual value of the parameter estimated. To implement the classical approach, it is necessary to quantify the closeness of an estimate to a parameter. One may rely on indices of absolute, relative, or squared error. Mean squared error (MSB) has often been used by statisticians, perhaps usually because of mathematical convenience. However, if estimators are evaluated using Monte Carlo simulation it is easy to use whatever criterion seems most reasonable in a given situation. 

The classical, frequentist approach in statistics requires the concept of the sampling distribution of an estimator. In classical statistics, a data set is commonly treated as a random sample from a population. Of course, in some situations the data actually have been collected according to a probability-sampling scheme. Whether that is the case or not, processes generating the data will be snbject to stochastic-ity and variation, which is a sonrce of uncertainty in nse of the data. Therefore, sampling concepts may be invoked in order to provide a model that accounts for the random processes, and that will lead to confidence intervals or standard errors. The population may or may not be conceived as a finite set of individnals. In some situations, such as when forecasting a fnture value, a continuous probability distribution plays the role of the popnlation. 

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