A new definition of the predictive likelihood

Siddhartha Chib; S. Rao Jammalamadaka; Ram C. Tiwari

doi:10.1016/0167-7152(87)90065-4

A new definition of the predictive likelihood

Siddhartha Chib
, S. Rao Jammalamadaka
, Ram C. Tiwari

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we present a widely applicable definition of the predictive likelihood based on estimators that are either sufficient or approximately sufficient. Under regularity conditions, this predictive likelihood is shown to equal the Bayes prediction density up to terms of order O_p(n^-1). For the cases where this predictive likelihood is difficult to compute, an approximate predictive likelihood is provided which differs from the proposed predictive likelihood by O_p(n^-1). To illustrate the ideas, the approximate predictive likelihood and the Bayes prediction density are obtained for a pth order non-circular autoregression.

Original language	English
Pages (from-to)	113-118
Number of pages	6
Journal	Statistics and Probability Letters
Volume	5
Issue number	2
DOIs	https://doi.org/10.1016/0167-7152(87)90065-4
State	Published - Mar 1987

Keywords

Bayes prediction density
approximate sufficiency
predictive likelihood
pth order non-circular autoregression

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abstract = "In this paper we present a widely applicable definition of the predictive likelihood based on estimators that are either sufficient or approximately sufficient. Under regularity conditions, this predictive likelihood is shown to equal the Bayes prediction density up to terms of order Op(n-1). For the cases where this predictive likelihood is difficult to compute, an approximate predictive likelihood is provided which differs from the proposed predictive likelihood by Op(n-1). To illustrate the ideas, the approximate predictive likelihood and the Bayes prediction density are obtained for a pth order non-circular autoregression.",

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AU - Tiwari, Ram C.

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N2 - In this paper we present a widely applicable definition of the predictive likelihood based on estimators that are either sufficient or approximately sufficient. Under regularity conditions, this predictive likelihood is shown to equal the Bayes prediction density up to terms of order Op(n-1). For the cases where this predictive likelihood is difficult to compute, an approximate predictive likelihood is provided which differs from the proposed predictive likelihood by Op(n-1). To illustrate the ideas, the approximate predictive likelihood and the Bayes prediction density are obtained for a pth order non-circular autoregression.

AB - In this paper we present a widely applicable definition of the predictive likelihood based on estimators that are either sufficient or approximately sufficient. Under regularity conditions, this predictive likelihood is shown to equal the Bayes prediction density up to terms of order Op(n-1). For the cases where this predictive likelihood is difficult to compute, an approximate predictive likelihood is provided which differs from the proposed predictive likelihood by Op(n-1). To illustrate the ideas, the approximate predictive likelihood and the Bayes prediction density are obtained for a pth order non-circular autoregression.

KW - Bayes prediction density

KW - approximate sufficiency

KW - predictive likelihood

KW - pth order non-circular autoregression

UR - https://www.scopus.com/pages/publications/45949125628

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VL - 5

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JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 2

ER -

A new definition of the predictive likelihood

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Keywords

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