Abstract: Suppose we have a random sample of size with multiple censoring. The exact Fisher information in the data is derived and expressed in terms of matrices when each block of censored data contains at least two order statistics. The results are applied to determine how much Fisher information about the location (scale) parameter is contained in the middle (two tails) of an ordered sample. The results show that, for Cauchy, Laplace, logistic, and normal distributions, the middle (extreme half) of the ordered data contains more than of the Fisher information about the location (scale) parameter. These results provide insight into the behavior of two well-known robust linear estimators of the location parameter.
Key words and phrases: Decomposition of Fisher information, limiting Pitman efficiency, location-scale family, matrix expression, multiply censored data.