Vector Exponential Models and Second Order Inference

D.A.S. Fraser, Uyen Hoang, Kexin Ji, Xufei Li, Li Li, Wei Lin, Jie Su

Abstract


For an exponential model with scalar parameter, WelchP:1963 examined the role of Bayesian analysis in statistical inference, more specifically the use of the Jeffreys:1946 prior. They determined that Bayesian intervals and thus in effect Bayesian quantiles had second order confidence accuracy. We use a Taylor series expansion of the log-model to develop a second order version of the vector exponential model; this is developed as a contribution to theory in statistics at a time when algorithms are prominent, and it provides a basis for generalizing the Welch-Peers approach to the vector parameter context.


Keywords


Asymptotic model; Bayes as approximate confidence; Exponential model; Jeffreys prior; Likelihood analysis; Root-information prior; Second order expansion.

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DOI: http://dx.doi.org/10.18187/pjsor.v8i3.518

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Title

Vector Exponential Models and Second Order Inference

Keywords

Asymptotic model; Bayes as approximate confidence; Exponential model; Jeffreys prior; Likelihood analysis; Root-information prior; Second order expansion.

Description

For an exponential model with scalar parameter, WelchP:1963 examined the role of Bayesian analysis in statistical inference, more specifically the use of the Jeffreys:1946 prior. They determined that Bayesian intervals and thus in effect Bayesian quantiles had second order confidence accuracy. We use a Taylor series expansion of the log-model to develop a second order version of the vector exponential model; this is developed as a contribution to theory in statistics at a time when algorithms are prominent, and it provides a basis for generalizing the Welch-Peers approach to the vector parameter context.


Date

2012-07-01

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol 8. No. 3, 2012



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810