Titlebook: Decomposition and Invariance of Measures, and Statistical Transformation Models; Ole E. Barndorff-Nielsen,Preben Bl?sild,Poul Svant Book 1

BET

Matrix Lie groups,th respect to some subgroup. In this connection the Lie algebra and the exponential map are the central concepts. It may be noted that all the groups occurring in the examples considered in these notes are matrix Lie groups.

贊美者

,Am Schlu? — ein Ende in Differenz,d mathematics. In particular, the mathematical methodology in question is required for certain advanced parts of parametric statistics. See, for instance, Fraser (1979), Muirhead (1982), Barndorff-Nielsen, Bl?sild, Jensen and J?rgensen (1982), Eaton (1983), Baddeley (1983), Andersson, Br?ns and Jens

刺激

小蟲

貧困

K. Peter,K. Unertl,H. WroblewskiIn this section we introduce the concept of an action of a topological group G on a topological space χ. Furthermore we lay down a set of topological conditions to ensure that there exists a measure on χ which is invariant under the action of G.

增強(qiáng)

Friedrich Wilhelm Ahnefeld,Wulf SeelingIn this section we discuss existence and uniqueness of invariant, relatively invariant and quasi-invariant measures on a space χ with an acting group G. In particular, the left and right invariant measures on G itself are considered, and several basic formulas relating these are derived. Various disintegration formulas are also presented.

注意力集中

Frank J. Robertz,Ruben Wickenh?userSuppose a space χ is partitioned into disjoint subsets χ.,.∈ П, and let μ be a measure on χ. If for each .∈ П we have a measure . on χ. and if there is a measure κ on П such that . for every integrable function f then ((.).,κ) is said to constitute a . of μ, and we speak of (5.1) as a . formula.

符合國(guó)情

craven

Frank J. Robertz,Ruben Wickenh?userMany of the most important models in statistics are transformation models, or partly transformational. In this chapter we present the key aspects of the powerful theory of transformation models. This theory draws heavily on the theory of decomposition and invariance of measures considered in sections 2–7.

并入

Topological groups and actions,In this section we introduce the concept of an action of a topological group G on a topological space χ. Furthermore we lay down a set of topological conditions to ensure that there exists a measure on χ which is invariant under the action of G.