Fisher Information: Nonstandard Situations

Abstract

AbstractFisher's measure of information is a fundamental concept in statistical science. It plays an important role in statistical theory of inference. The definition and applications of Fisher information in standard inference based on random samples have been discussed extensively in the literature. The Fisher information in nonstandard situations involving ordered data has recently attracted considerable attention with discussions focusing on Fisher information in order statistics, percentiles, randomly censored data, concomitants, progressively censored data, and record values, with numerous applications including optimal linear estimates, characterizations, ranked set sampling, and genetic studies. Direct calculation of Fisher information in these nonstandard situations is tedious and computationally difficult. Main techniques to simplify the calculation are discussed here with many examples. Finally, some applications of Fisher information in ordered data are also highlighted.