A small mean squared error can be obtained by focusing on rules that are functions of one of these things, according to the Rao-Blackwell theorem. A complete, sufficient one of these things is independent of an ancillary one according to Basu's theorem. The factorization theorem uses the conditional of a random variable given one of these things to determine whether they are sufficient. These things can be detangled from nuisance parameters, which is possible to do by using the likelihood function, which itself is used to generate (*) estimators. These things can be calculated from an observed frequency distribution, distinguishing them from parameters, which are measures of a probability distribution. For 10 points
A small mean squared error can be obtained by focusing on rules that are functions of one of these things, according to the Rao-Blackwell theorem. A complete, sufficient one of these things is independent of an ancillary one according to Basu's theorem. The factorization theorem uses the conditional of a random variable given one of these things to determine whether they are sufficient. These things can be detangled from nuisance parameters, which is possible to do by using the likelihood function, which itself is used to generate (*) estimators. These things can be calculated from an observed frequency distribution, distinguishing them from parameters, which are measures of a probability distribution. For 10 points, name these measures of a sample, such as the variance, range, and mean.
A small mean squared error can be obtained by focusing on rules that are functions of one of these things, according to the Rao-Blackwell theorem.
statistic [or sufficient statistic; until they are read, prompt on: statistical parameter, statistical estimator]