The Information Content of Observations, and Asymptotically Sufficient Statistics

Expressions and estimates are given for the quantity of information contained in observations with respect to an estimated parameter for a fixed and a random number of observations. Conditions are indicated under which the maximum-likelihood, Pitman, and other estimates are asymptotically sufficient statistics (i.e., estimates in which the quantity of information about the estimates parameter coincides with the quantity of information in the observations.