Download e-book for kindle: Information and Exponential Families: In Statistical Theory by O. Barndorff-Nielsen

By O. Barndorff-Nielsen

ISBN-10: 1118857283

ISBN-13: 9781118857281

ISBN-10: 111885750X

ISBN-13: 9781118857502

First released by way of Wiley in 1978, this publication is being re-issued with a brand new Preface by way of the writer. The roots of the e-book lie within the writings of RA Fisher either as issues effects and the overall stance to statistical technological know-how, and this stance was once the deciding on think about the author's choice of issues. His treatise brings jointly effects on facets of statistical info, significantly referring to chance services, plausibility services, ancillarity, and sufficiency, and on exponential households of likelihood distributions. 

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Additional info for Information and Exponential Families: In Statistical Theory

Example text

This model was studied by Sverdrup (1965). It follows from (3) that the parameters p,

To prove this, suppose t is B-sufficient, let A be any event and set B = { M ( A ; •) = 1} where M(-; •) is the common Markov kernel. By assumption, M(A; ) = and consequently \ B = \ A [^P], as was to be verified. Let t and u be statistics, assume that t is B-suflicient, and let M denote the Markov kernel for the common conditional distribution given t. In the case t and 46 Logic of Inferential Separation, Ancillarity and Sufficiency u are independent under a P e $ , then for any P(C) = P(C\t) = M(C;) Cea(u) pp].

Then t is sufficient for x with respect to ip if (^P', x) is nonformative with respect to More generally, if t is ancillary or sufficient with respect to i//, as above, it will also be called ancillary respectively sufficient with respect to any parameter function which depends on ij/ only. In connection with the discussion of S-ancillarity and S-sufficiency it is convenient to introduce the concept of a cut. Let t be a statistic. e. one has a mapping on ty into ^P, x given by P -> (Pt, P*). Now, t is said to be a cut if this mapping is actually onto % x or, in other words, if any of the marginal distributions of t combined with any of the conditional distributions given t gives a probability measure in Clearly, if t is B-ancillary or B-sufficient then t is a cut.

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Information and Exponential Families: In Statistical Theory by O. Barndorff-Nielsen

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