Exponentielle Familien, Suffizienz und das Theorem von Darmois-Koopman-Pitman

Harald Führer
2019 unpublished
This diploma thesis deals with the classical theorem of (Fisher-)Darmois-Koopman-Pitman. Three papers by G. Darmois, B. O. Koopman and E. J. G. Pitman from 1935/36 have published this theorem independently of one another, building on the works of R. A. Fisher. The present work analyzes these three classical works. Their content is presented and compared with contempoary statistical theory. An overview of the theory takes place from today's perspective. In addition to basic concepts of
more » ... ncepts of measurement and probability theory, statistical foundations are presented. Exponential families as well as sufficient statistics are presented in detail. In addition, a brief presentation of point estimation is given in terms of expectation, Fisher information, and maximum likelihood. The main part of the diploma thesis is the analysis of the work of G. Darmois, B. O. Koopman and E. J. G. Pitman, as well as the preliminary work of R. A. Fisher.
doi:10.25365/thesis.60309 fatcat:6stsyop7ajdmxbnfo3o24hev4y