ABSTRACT
This chapter discusses how to “guess” the parameter of a statistical model. For any realization of a random sample, estimates lead to realizations of the estimators. Estimators are random variables, whereas estimates are realizations of random variables. The chapter shows how to construct estimators and looks at a general principle that can be applied to any statistical model to derive general results about properties of a large class of estimators. The maximum likelihood approach prescribes how to find the value of a parameter that maximizes the likelihood function. The chapter also discusses the unbiased estimator with the lowest variance, which is called the best unbiased estimator, and provides the procedure for finding best unbiased estimators. Estimators can be judged in different ways, for example, on the basis of best unbiased estimator or the mean squared error.
