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Regression Calibration in Measurement Error Modeling Song, Weixing
Description
When a p-dimensional parameter θ is defined through the moment condition Em(X,θ) = 0, a simple estimation procedure of θ is proposed by Hong and Tamer when X, a k-dimensional random vector, is contaminated with Laplace measurement error U, that is, we can only observe Z = X + U. However, the estimation procedure was designed particularly for the cases where the components of the measurement error vector U are independent. We shall introduce a general multivariate Laplace distribution, then extend the Hong-Tamer moment estimation procedure to a more general multivariate scenario. Moreover, the Hong-Tamer moment estimation procedure is based on the unconditional expectation Em(X,θ) = EH(Z,θ) for some function H. Example shows this techniques does not work in some cases. We will further discuss an estimation procedure based on the condition expectation E(m(X,θ)|Z), which can be treated as an extension of the regression calibration technique. Large sample properties of the proposed estimation procedure will be investigated. Next, I will try to extend the above extended regression technique to nonparametric setup, particularly focusing on the normal and Laplace measurement error.
Item Metadata
Title |
Regression Calibration in Measurement Error Modeling
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2016-08-17T09:30
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Description |
When a p-dimensional parameter θ is defined through the moment condition Em(X,θ) = 0, a simple estimation procedure of θ is proposed by Hong and Tamer when X, a k-dimensional random vector, is contaminated with Laplace measurement error U, that is, we can only observe Z = X + U. However, the estimation procedure was designed particularly for the cases where the components of the measurement error vector U are independent. We shall introduce a general multivariate Laplace distribution, then extend the Hong-Tamer moment estimation procedure to a more general multivariate scenario. Moreover, the Hong-Tamer moment estimation procedure is based on the unconditional expectation Em(X,θ) = EH(Z,θ) for some function H. Example shows this techniques does not work in some cases. We will further discuss an estimation procedure based on the condition expectation E(m(X,θ)|Z), which can be treated as an extension of the regression calibration technique. Large sample properties of the proposed estimation procedure will be investigated. Next, I will try to extend the above extended regression technique to nonparametric setup, particularly focusing on the normal and Laplace measurement error.
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Extent |
40 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Kansus State University
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Series | |
Date Available |
2017-02-15
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0342800
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International