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

• 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
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2011.08.011

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.