Skip to main content

Advertisement

Log in

Empirical estimates for heteroscedastic hierarchical dynamic normal models

  • Research Article
  • Published:
Journal of the Korean Statistical Society Aims and scope Submit manuscript

Abstract

The available heteroscedastic hierarchical models perform well for a wide range of real-world data, but for data sets that exhibit a dynamic structure they seem fit poorly. In this work, we develop a two-level dynamic heteroscedastic hierarchical model and suggest some empirical estimators for the association hyper-parameters. Moreover, we derive the risk properties of the estimators. Our proposed model has the feature that the dependence structure among observations is produced from the hidden variables in the second level and not through the observations themselves. The comparison between various empirical estimators is illustrated through a simulation study. Finally, we apply our methods to a baseball data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Barboza, L., Li, B., Tingely, M., & Viens, F. (2014). Reconstructing past climate from natural proxies and estimated climate forcings using short- and long-memory models. Annals of Applied Statistics, 8, 1966–2001.

    Article  MathSciNet  Google Scholar 

  • Berger, J., & Strawderman, W. E. (1996). Choice of hierarchical priors: Admissibility in estimation of normal means. Annals of Statistics, 24, 931–951.

    Article  MathSciNet  Google Scholar 

  • Bhattacharya, A., Pati, D., Pillai, N. S., & Dunson, D. B. (2014). Dirichlet-Laplace priors for optimal shrinkage. arXiv:1401.5398v1.

  • Brown, L. D. (2008). In-season prediction of batting average: A field test of empirical Bayes and Bayes methodologies. The Annals of Applied Statistics, 2, 113–152.

    Article  MathSciNet  Google Scholar 

  • Brown, L. D., & Greenshtein, E. (2009). Nonparametric empirical Bayes and compound decision approaches to estimation of a high-dimensional vector of means. Annals of Statistics, 37, 1685–1704.

    Article  MathSciNet  Google Scholar 

  • Efron, B., & Morris, C. (1973). Stein’s estimation rule and its competitors: An empirical Bayes approach. Journal of the American Statistical Association, 68, 117–130.

    MathSciNet  MATH  Google Scholar 

  • Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models. Bayesian Analysis, 1, 515–533.

    MathSciNet  MATH  Google Scholar 

  • Ghoreishi, S. K. (2017). Bayesian analysis of hierarchical heteroscedastic linear models using Dirichlet-Laplace priors. Journal of Statistical Theory and Applications, 16(1), 53–64.

    Article  MathSciNet  Google Scholar 

  • Ghoreishi, S. K., & Meshkani, M. R. (2014). On SURE estimators in hierarchical models assuming heteroscedasticity for both levels of a two-level normal hierarchical model. Journal of Multivariate Analysis, 132, 129–137.

    Article  MathSciNet  Google Scholar 

  • Grish, K., & Chien, S. (2017). Macrophage differentiation in normal and accelerated wound healing. In Macrophages (pp. 353–364). Cham: Springer.

  • James, W., & Stein, C. M. (1961). Estimation with quadratic loss. In Proceedings of the 4th Berkeley symposium on probability and statistics (Vol. 1, pp. 367–379).

  • Li, K. C. (1986). Asymptotic optimality of \(C_L\) and generalized cross validation in ridge regression with application to spline smoothinge. Annals of Statistics, 14, 1101–1112.

    Article  MathSciNet  Google Scholar 

  • Li, B., Nychka, D. W., & Ammann, C. M. (2010). The value of multi-proxy reconstruction of past climate. Journal of the American Statistical Association, 105, 883–911.

    Article  MathSciNet  Google Scholar 

  • Shand, L., Li, B., Park, T., & Albraccin, D. (2018). Spatially varying auto-regressive models for prediction of new human immunodeficiency virus diagnoses. Journal of Royal Statistical Society Series C, 67, 1003–1022.

    Article  MathSciNet  Google Scholar 

  • Stein, C. M. (1962). Confidence sets for the mean of a multivariate normal distribution (with discussion). The Journal of the Royal Statistical Society, Series B, 24, 265–296.

    MathSciNet  MATH  Google Scholar 

  • Xie, X., Kou, S. C., & Brown, L. D. (2012). SURE estimates for a heteroscedastic hierarchical model. Journal of the American Statistical Association, 107, 1465–1479.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. K. Ghoreishi.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ghoreishi, S.K., Wu, J. Empirical estimates for heteroscedastic hierarchical dynamic normal models. J. Korean Stat. Soc. 50, 528–543 (2021). https://doi.org/10.1007/s42952-020-00093-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42952-020-00093-2

Keywords

Mathematics Subject Classification

Navigation