Elimination of Nuisance Parameters
Elimination of Nuisance Parameters
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DOI：
10.1007/978-1-4612-3894-2_7
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
J. Ghosh
中科院分区：
文献类型：
--
作者：
J. Ghosh
The problem begins with an unknown state of nature represented by the parameter of interest θ . We have some information about θ to begin with — e.g., we know that θ is a member of some well-defined parameter space θ- but we are seeking more. Toward this end, a statistical experiment & is planned and performed and this generates the sample observation x. Further information about θ is then obtained by a careful analysis of the data ( &, x) in the light of all our prior information about θ and in the context of the particular inference problem related to θ . For going through the rituals of the traditional sample-space analysis of data, we must begin with the invocation of a trinity of abstractions (X, A, P), whereXis the sample space,Ais aσ-algebra of events (subsets ofX), andPis a family of probability measures onA. If the model (X, A, P) is such that we can represent the familyPas {Pθ: θ εθ}, where the correspondence θ → Pθis one-one and (preferably) smooth, then we go about analyzing the data according to our own light and are thankful for not having to contend with any nuisance parameters.
