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Contiguity of probability measures: ...

Roussas, George G.

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Contiguity of probability measures: some applications in statistics

Record Type:	Electronic resources : Monograph/item
Title/Author:	Contiguity of probability measures: some applications in statistics/ George G. Roussas.
Author:	Roussas, George G.
Published:	Cambridge :Cambridge University Press, : 1972.,
Description:	xiii, 248 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
[NT 15003449]:	On the concept of contiguity and related theorems -- Asymptotic expansions and asymptotic distribution of likelihood functions -- Approximation of a given family of probability measures by an exponential family, asymptotic sufficiency -- Some statistical applications, AUMP and AUMPU test for certain testing hypotheses problems -- Some statistical applications, asymptotic efficiency of estimates -- Multiparameter asymptotically optimal tests.
Subject:	Probability measures. -
Online resource:	https://doi.org/10.1017/CBO9780511804373
ISBN:	9780511804373

Contiguity of probability measures: some applications in statistics
Roussas, George G.

Contiguity of probability measures: some applications in statistics[electronic resource] /George G. Roussas. - Cambridge :Cambridge University Press,1972. - xiii, 248 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;63. - Cambridge tracts in mathematics ;63..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

On the concept of contiguity and related theorems -- Asymptotic expansions and asymptotic distribution of likelihood functions -- Approximation of a given family of probability measures by an exponential family, asymptotic sufficiency -- Some statistical applications, AUMP and AUMPU test for certain testing hypotheses problems -- Some statistical applications, asymptotic efficiency of estimates -- Multiparameter asymptotically optimal tests.

This Tract presents an elaboration of the notion of 'contiguity', which is a concept of 'nearness' of sequences of probability measures. It provides a powerful mathematical tool for establishing certain theoretical results with applications in statistics, particularly in large sample theory problems, where it simplifies derivations and points the way to important results. The potential of this concept has so far only been touched upon in the existing literature, and this book provides the first systematic discussion of it. Alternative characterizations of contiguity are first described and related to more familiar mathematical ideas of a similar nature. A number of general theorems are formulated and proved. These results, which provide the means of obtaining asymptotic expansions and distributions of likelihood functions, are essential to the applications which follow.

ISBN: 9780511804373Subjects--Topical Terms:

686648
Probability measures.

LC Class. No.: QA273.43 / .R68 1972

Dewey Class. No.: 519.2

Contiguity of probability measures: some applications in statistics
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100 1 $a Roussas, George G. $3 532727
245 1 0 $a Contiguity of probability measures: some applications in statistics $h [electronic resource] / $c George G. Roussas.
260 $a Cambridge : $b Cambridge University Press, $c 1972.
300 $a xiii, 248 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge tracts in mathematics ; $v 63
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a On the concept of contiguity and related theorems -- Asymptotic expansions and asymptotic distribution of likelihood functions -- Approximation of a given family of probability measures by an exponential family, asymptotic sufficiency -- Some statistical applications, AUMP and AUMPU test for certain testing hypotheses problems -- Some statistical applications, asymptotic efficiency of estimates -- Multiparameter asymptotically optimal tests.
520 $a This Tract presents an elaboration of the notion of 'contiguity', which is a concept of 'nearness' of sequences of probability measures. It provides a powerful mathematical tool for establishing certain theoretical results with applications in statistics, particularly in large sample theory problems, where it simplifies derivations and points the way to important results. The potential of this concept has so far only been touched upon in the existing literature, and this book provides the first systematic discussion of it. Alternative characterizations of contiguity are first described and related to more familiar mathematical ideas of a similar nature. A number of general theorems are formulated and proved. These results, which provide the means of obtaining asymptotic expansions and distributions of likelihood functions, are essential to the applications which follow.
650 0 $a Probability measures. $3 686648
650 0 $a Mathematical statistics. $3 516858
830 0 $a Cambridge tracts in mathematics ; $v 63. $3 3470581
856 4 0 $u https://doi.org/10.1017/CBO9780511804373