دانلود کتاب Introduction to the theory of regular exponential families

PrefaceThe first version of these notes appeared in 1970 when I lecturedon exponential families on the basis of some notes written by OleBarndorff - Nielsen and Anders Holst Andersen.A Danish version appeared in 1976 in connection with a graduatecourse in statistics and the present version is essentially atranslation of this.In the meantime the excellent book by Barndorff - Nielsen (1978)has appeared. The present notes differ in the choice of materialin that I have concentrated On the algebraic aspects,of the regu-lar models and then added the classical application of the NeymanPearson theory as well as the asymptotic theory, without which itis difficult to apply any of the models.I have benefitted from a visit to Lund (1972) and to Goteborg(1976) where I presented the topic in a series of lectures. Iwelcome the opportunity to thank Gunnar Blom and Peter Jagersfor the invitation and for hospitality during the visits.Another main source of inspiration has been the lecture notes byPer Martin - LOf (1970) who has developed the exponential familiesand their statistical analysis from the point of view of stati-stical mechanics. This point of view has not been adopted here. Ashort account can be found in Per Martin - Löf (1974).The lecture notes by Søren Tolver Jensen (1978) have helped meclarify the formulation of the case of a singular covariance ma-trix, see section 7.Anders Hald and Steffen Lauritzen have carefully read the manu-script in one of its previous versions with the result that someformulations were improved and others corrected. Vivi Nielsen hastyped the final manuscript. Thus it will be apparent that I haveborrowed all the material from other sources and have had expertsto check the presentation. My only contributions if any thus liesin the initiative plus the remaining errors.Copenhagen, February 1979Søren Johansen