Locally quadratic log likelihood and data-based transformations

Ian R. Harris; Donna K. Pauler

doi:10.1080/03610929208830804

Locally quadratic log likelihood and data-based transformations

Ian R. Harris, Donna K. Pauler

Urology

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

4 Scopus citations

Abstract

The investigation of multi-parameter likelihood functions is simplified if the log likelihood is quadratic near the maximum, as then normal approximations to the likelihood can be accurately used to obtain quantities such as likelihood regions. This paper proposes that data-based transformations of the parameters can be employed to make the log likelihood more quadratic, and illustrates the method with one of the simplest bivariate likelihoods, the normal two-parameter likelihood.

Original language	English (US)
Pages (from-to)	637-646
Number of pages	10
Journal	Communications in Statistics - Theory and Methods
Volume	21
Issue number	3
DOIs	https://doi.org/10.1080/03610929208830804
State	Published - Jan 1 1992

Keywords

data-based parametrization
normal likelihood
quadratic log likelihood

ASJC Scopus subject areas

Statistics and Probability

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10.1080/03610929208830804

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title = "Locally quadratic log likelihood and data-based transformations",

abstract = "The investigation of multi-parameter likelihood functions is simplified if the log likelihood is quadratic near the maximum, as then normal approximations to the likelihood can be accurately used to obtain quantities such as likelihood regions. This paper proposes that data-based transformations of the parameters can be employed to make the log likelihood more quadratic, and illustrates the method with one of the simplest bivariate likelihoods, the normal two-parameter likelihood.",

keywords = "data-based parametrization, normal likelihood, quadratic log likelihood",

author = "Harris, {Ian R.} and Pauler, {Donna K.}",

note = "Funding Information: This research has been supported by the National Science Foundation, Grant DMS-8802722. The authors would also like to thank Carl Morris for stimulating their interest in this area, and an anonymous referee for many helpful suggestions.",

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AU - Pauler, Donna K.

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PY - 1992/1/1

Y1 - 1992/1/1

N2 - The investigation of multi-parameter likelihood functions is simplified if the log likelihood is quadratic near the maximum, as then normal approximations to the likelihood can be accurately used to obtain quantities such as likelihood regions. This paper proposes that data-based transformations of the parameters can be employed to make the log likelihood more quadratic, and illustrates the method with one of the simplest bivariate likelihoods, the normal two-parameter likelihood.

AB - The investigation of multi-parameter likelihood functions is simplified if the log likelihood is quadratic near the maximum, as then normal approximations to the likelihood can be accurately used to obtain quantities such as likelihood regions. This paper proposes that data-based transformations of the parameters can be employed to make the log likelihood more quadratic, and illustrates the method with one of the simplest bivariate likelihoods, the normal two-parameter likelihood.

KW - data-based parametrization

KW - normal likelihood

KW - quadratic log likelihood

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Locally quadratic log likelihood and data-based transformations

Abstract

Keywords

ASJC Scopus subject areas

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