On estimation of a heteroscedastic measurement error model under heavy-tailed distributions

It is common in epidemiology and other fields that the analyzing data is collected with error-prone observations and the variances of the measurement errors change across observations. Heteroscedastic measurement error (HME) models have been developed for such data. This paper extends the structural...

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Bibliographic Details
Published in:Computational statistics & data analysis 2012-02, Vol.56 (2), p.438-448
Main Authors: Cao, Chun-Zheng, Lin, Jin-Guan, Zhu, Xiao-Xin
Format: Article
Language:English
Subjects:
Applications
Asymptotic properties
Computer simulation
Data processing
EM algorithm
Equation error
Error analysis
Errors
Exact sciences and technology
Exact solutions
General topics
Heteroscedastic measurement error
Heteroscedastic measurement error Scale mixtures of normal distribution Maximum likelihood EM algorithm Equation error
Mathematical analysis
Mathematics
Maximum likelihood
Medical sciences
Multivariate analysis
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Probability and statistics
Scale mixtures of normal distribution
Sciences and techniques of general use
Statistics
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Summary:It is common in epidemiology and other fields that the analyzing data is collected with error-prone observations and the variances of the measurement errors change across observations. Heteroscedastic measurement error (HME) models have been developed for such data. This paper extends the structural HME model to situations in which the observations jointly follow scale mixtures of normal (SMN) distribution. We develop the EM algorithm to compute the maximum likelihood estimates for the model with and without equation error respectively, and derive closed forms of asymptotic variances. We also conduct simulations to verify the effective of the EM estimates and confirm their robust behaviors based on heavy-tailed SMN distributions. A practical application is reported for the data from the WHO MONICA Project on cardiovascular disease.
ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2011.08.011