ABSTRACT

In this chapter we give a compact survey of statistical inference based on a random sample. Concretely speaking, we introduce the idea of su±cient statistics and construct minimum variance unbiased estimators by using them. Furthermore, we derive the Cram¶er-Rao bound which gives a lower bound for the variance of unbiased estimators, and discuss the e±cient estimator which achieves it. Heretofore, we discussed approaches in random samples with ¯xed size n. In these cases it is often di±cult to obtain the exact distribution of estimators from samples of size n. However, if the sample sizes are \large", then the structure of estimation becomes clearer and simpler. Therefore, we de¯ne \goodness" in asymptotic inference theory and describe the asymptotic optimality of estimators.