Heteroscedastic replicated measurement error models under asymmetric heavy-tailed distributions

• Published in: Computational statistics Vol. 33; no. 1; pp. 319 - 338
• Main Authors: Cao, Chunzheng, Chen, Mengqian, Wang, Yahui, Shi, Jian Qing
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2018; Springer Nature B.V
• Subjects: Bayesian analysis; Computer simulation; Data analysis; Economic Theory/Quantitative Economics/Mathematical Methods; Empirical equations; Error analysis; Mathematics and Statistics; Maximum likelihood estimates; Measurement errors; Original Paper; Outliers (statistics); Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Skewed distributions; Statistics; Robustness; Maximum likelihood estimates; Scale mixtures of skew-normal distributions; EM algorithm
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-017-0720-8

We propose a heteroscedastic replicated measurement error model based on the class of scale mixtures of skew-normal distributions, which allows the variances of measurement errors to vary across subjects. We develop EM algorithms to calculate maximum likelihood estimates for the model with or without equation error. An empirical Bayes approach is applied to estimate the true covariate and predict the response. Simulation studies show that the proposed models can provide reliable results and the inference is not unduly affected by outliers and distribution misspecification. The method has also been used to analyze a real data of plant root decomposition.