Fisher Information in Order Statistics
研究了独立同分布观测中费希尔信息在次序统计量间的分布，提出一种分解方法简化计算，并推导递推关系，最终将多重积分简化为单积分求和，便于实际应用。
Abstract When we have n independently and identically distributed observations, it is an interesting question how the Fisher information is distributed among order statistics. The recipe for the Fisher information in order statistics is easy, but the detailed calculation has been known to be complicated. An indirect approach, using a decomposition of the Fisher information in order statistics, simplifies the calculation. Some recurrence relations for the Fisher information in order statistics are derived that facilitate the calculation. The Fisher information in the first r order statistics is an r multiple integral, but it can be simplified to just a double integral by using the decomposition. A recurrence relation further simplifies the double integral to a sum of single integrals. An “information plot” is suggested, from which we can read at once the Fisher information in any set of consecutive order statistics for a parametric distribution.