Characterization Theorems when Variables Are Measured with Error

John P Holcomb

doi:10.1006/jmva.1998.1796

Characterization Theorems when Variables Are Measured with Error

John P Holcomb

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

Abstract

Linear regression models are studied when variables of interest are observed in the presence of measurement error. Techniques involving Fourier transforms that lead to simple differential equations with unique solutions are used in the context of multiple regression. Necessary and sufficient conditions are proven for a random vector of measurement error of the independent variable to be multivariate normal. One characterization involves the Fisher score of the observed vector. A second characterization involves the Hessian matrix of the observed density.

Original language	American English
Journal	Journal of Multivariate Analysis
Volume	68
DOIs	https://doi.org/10.1006/jmva.1998.1796
State	Published - Feb 1 1999

Keywords

Measurement error model; conditional expectation; conditional variance

Disciplines

Multivariate Analysis

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10.1006/jmva.1998.1796License: CC BY

Cite this

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title = "Characterization Theorems when Variables Are Measured with Error",

abstract = " Linear regression models are studied when variables of interest are observed in the presence of measurement error. Techniques involving Fourier transforms that lead to simple differential equations with unique solutions are used in the context of multiple regression. Necessary and sufficient conditions are proven for a random vector of measurement error of the independent variable to be multivariate normal. One characterization involves the Fisher score of the observed vector. A second characterization involves the Hessian matrix of the observed density.",

keywords = "Measurement error model; conditional expectation; conditional variance",

author = "Holcomb, \{John P\}",

note = "Holcomb, J. P. (1999). Characterization Theorems when Variables Are Measured with Error. Journal of Multivariate Analysis, 68(2), 283-298. doi:10.1006/jmva.1998.1796",

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N2 - Linear regression models are studied when variables of interest are observed in the presence of measurement error. Techniques involving Fourier transforms that lead to simple differential equations with unique solutions are used in the context of multiple regression. Necessary and sufficient conditions are proven for a random vector of measurement error of the independent variable to be multivariate normal. One characterization involves the Fisher score of the observed vector. A second characterization involves the Hessian matrix of the observed density.

AB - Linear regression models are studied when variables of interest are observed in the presence of measurement error. Techniques involving Fourier transforms that lead to simple differential equations with unique solutions are used in the context of multiple regression. Necessary and sufficient conditions are proven for a random vector of measurement error of the independent variable to be multivariate normal. One characterization involves the Fisher score of the observed vector. A second characterization involves the Hessian matrix of the observed density.

KW - Measurement error model; conditional expectation; conditional variance

UR - https://engagedscholarship.csuohio.edu/scimath_facpub/28

UR - http://journals.ohiolink.edu/ejc/article.cgi?issn=0047259x&issue=v68i0002&article=283_ctwvamwe

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DO - 10.1006/jmva.1998.1796

M3 - Article

VL - 68

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

ER -

Characterization Theorems when Variables Are Measured with Error

Abstract

Keywords

Disciplines

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