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Cramér-Rao inequality revisited. (English) Zbl 1453.62018

Summary: Among C R Rao’s many contributions to statistical inference, one which has been and still is considered to be of extreme importance in the areas of statistics, physics and of signal processing in electrical engineering beside other sciences is an inequality which is now known as the Cramér-Rao inequality. This result was studied in recent years by several other scientists to relax the conditions under which it holds and to generalize it in different directions. Contributions by A. Bhattacharyya [Sankhyā 8, 1–14 (1948; Zbl 0038.29603)], E. W. Barankin [Ann. Math. Stat. 20, 477–501 (1949; Zbl 0034.23002)] and V. Fabian and J. Hannan [Ann. Stat. 5, 197–205 (1977; Zbl 0358.62030)] are significant in this area. We do not propose to give an extensive survey of results connected with the inequality. Our aim in this communication is to highlight some recent advances.

MSC:

62-03 History of statistics
01A60 History of mathematics in the 20th century
01A70 Biographies, obituaries, personalia, bibliographies
62F10 Point estimation
62G30 Order statistics; empirical distribution functions
60E15 Inequalities; stochastic orderings

Biographic References:

Rao, Calyampudi Radhakrishna
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References:

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