165
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Bayesian inference in a heteroscedastic replicated measurement error model using heavy-tailed distributions

, , &
Pages 2915-2928 | Received 23 Nov 2016, Accepted 27 Jun 2017, Published online: 08 Jul 2017

References

  • Fuller WA. Measurement error models. New York: Wiley; 1974.
  • Cheng CL, Van Ness JW. Statistical regression with measurement error. London: Arnold; 1999.
  • Carroll RJ, Ruppert D, Stefanski LA, et al. Measurement error in nonlinear models: a modern perspective. 2nd ed. Boca Raton, FL: Chapman & Hall; 2006.
  • Kulathinal SB, Kuulasmaa K, Gasbarra D. Estimation of an errors-in-variables regression model when the variances of the measurement errors vary between the observations. Stat Med. 2002;21(8):1089–1101.
  • Cheng CL, Riu J. On estimating linear relationships when both variables are subject to heteroscedastic measurement errors. Technometrics. 2006;48(4):511–519.
  • Patriota AG, Bolfarine H, de Castro M. A heteroscedastic structural errors-in-variables model with equation error. Stat Methodol. 2009;6:408–423.
  • McAssey MP, Hsieh F. Slope estimation in structural line-segment heteroscedastic measurement error models. Stat Med. 2010;29:2631–2642.
  • Reiersol O. Identifiability of a linear relation between variables which are subject to errors. Econometrica. 1950;18(4):375–389.
  • Spiegelman D, Logan R, Grove D. Regression calibration with heteroscedastic error variance. Int J Biostat. 2011;7(1):1–34.
  • Guo Y, Little RJ. Regression analysis with covariates that have heteroscedastic measurement error. Stat Med. 2011;30(18):2278–2294.
  • de Castro M, Bolfarine H, Galea M. Bayesian inference in measurement error models for replicated data. Environmetrics. 2013;24(1):22–30.
  • Andrews DF, Mallows CL. Scale mixtures of normal distributions. J R Stat Soc B. 1974;36(1):99–102.
  • de Castro M, Galea M. Robust inference in an heteroscedastic measurement error model. J Korean Stat Soc. 2010;39(4):439–447.
  • Cao C-Z, Lin J-G, Zhu X-X. On estimation of a heteroscedastic measurement error model under heavy-tailed distributions. Comput Stat Data Anal. 2012;56(2):438–448.
  • Lin J-G, Cao C-Z. On estimation of measurement error models with replication under heavy-tailed distributions. Comput Stat. 2013;28(2):809–829.
  • Cao CZ, Lin JG, Shi JQ, et al. Multivariate measurement error models for replicated data under heavy-tailed distributions. J Chemometr. 2015;29(8):457–466.
  • Fang KT, Kotz S, Ng KW. Symmetrical multivariate and related distributions. London: Chapman and Hall; 1990.
  • Lange K, Sinsheimer JS. Normal/independent distributions and their applications in robust regression. J Comput Graph Stat. 1993;2(2):175–198.
  • De la Cruz R. Bayesian analysis for nonlinear mixed-effects models under heavy-tailed distributions. Pharm Stat. 2014;13:81–93.
  • Cabral CRB, Lachos VH, Madruga MR. Bayesian analysis of skew-normal independent linear mixed models with heterogeneity in the random-effects population. J Stat Plan Inference. 2012;142(1):181–200.
  • Garay AM, Bolfarine H, Lachos VH, et al. Bayesian analysis of censored linear regression models with scale mixtures of normal distributions. J Appl Stat. 2015;42(12):2694–2714.
  • Kelly BC. Some aspects of measurement error in linear regression of astronomical data. Astrophys J. 2007;665:1489–1506.
  • Gelman A.Prior distributions for variance parameters in hierarchical models. Bayesian Anal. 2006; 1(3):515–534.
  • Liu C. Bayesian robust multivariate linear regression with incomplete data. J Amer Stat Assoc. 1996;91:1219–1227.
  • Gelfand AE, Dey DK, Chang H. Model determination using predictive distributions with implementation via sampling based methods (with discussion). In: Bernardo JM, Berger JO, Dawid AP, et al, editors. Bayesian statistics 4. Oxford: Oxford University Press; 1992. p. 147–167.
  • Spiegelhalter DJ, Best NG, Carlin BP, et al. Bayesian measures of model complexity and fit (with discussion). J R Stat Soc B. 2002;64(4):583–639.
  • Barndorff-Nielsen OE. Normal inverse Gaussian distributions and stochastic volatility modelling. Scand J Stat. 1997;24:1–13.
  • Hobert J, Casella G. The effect of improper priors on Gibbs sampling in hierarchical linear mixed models. J AM Stat Assoc. 1996;91:1461–1473.
  • Geweke J. Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. Bernardo JM, Berger JO, Dawid AP, et al., editors. Bayesian statistics, Vol. 4. Oxford: Oxford University Press; 1992. p. 169–193.
  • Zhang XY, Wang W. The decomposition of fine and coarse roots: their global patterns and controlling factors. Sci Rep. 2015;5:9940.
  • Lachos VH, Bandyopadhyay D, Dey DK. Linear and nonlinear mixed-effects models for censored HIV viral loads using normal/independent distributions. Biometrics. 2011;67(4):1594–1604.
  • Lachos VH, Angolini T, Abanto-Valle CA. On estimation and local influence analysis for measurement errors models under heavy-tailed distributions. Stat Pap. 2011; 52:567–590.
  • Ferguson TS. A Bayesian analysis of some nonparametric problems. Ann Stat. 1973;1(2):209–230.
  • Phadia EG. Prior processes and their applications. New York: Springer; 2013.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.