Article Sidebar

Download
PDF
Statistic
Read Counter : 363 Download : 347

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Main Article Content

Abstract

Rank-based analysis of linear models is based on selecting an appropriate score function. The information about the shape of the underlying distribution is necessary for the optimal selection; leading towards asymptotically efficient analysis. In this study, we analyzed the multilevel model with cluster-correlated error terms following a family of skew-t distribution with the rank-based approach based on score function derived for the class of skew-normal distribution. The rank fit is compared with the Restricted Maximum Likelihood (REML) estimation in terms of validity and efficiency for different sample sizes. A Monte Carlo simulation study is carried out over skewed-t and contaminated-t distribution with a range of skewness parameters from moderately to highly skewed. The standard error of regression coefficients is significantly reduced in the rank-based approach and further reduces for a large sample size. Rank-based fit appeared asymptotically efficient than REML for each shape parameter of skewness in skew-t and contaminated-t distribution computed through a calculation of precision. The empirical validity of fixed effects is obtained up to the nominal level 0.95 in REML but not rank-based with skew-normal score function.

Keywords

Multilevel models Rank-based REML Skew-normal Skew-t

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors who publish with this journal agree to the following License

CC BY: This license allows reusers to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given to the creator. The license allows for commercial use.

 

How to Cite
Saleem, S., & Sherwani, R. A. K. (2021). Efficient Rank-Based Analysis of Multilevel Models for the Family of Skew-t Errors. Pakistan Journal of Statistics and Operation Research, 17(1), 89-98. https://doi.org/10.18187/pjsor.v17i1.3339
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. Al-shomrani, A. A. (2003). A Comparison of Different Schemes for Selecting and Estimating Score Functions Based on Residuals [Western Michigan University].
  2. Arellano-Valle, R. B., & Azzalini, A. (2013). The centred parameterization and related quantities of the skew-t distribution. Journal of Multivariate Analysis, 113, 73-90.
  3. Auda, H. A., McKean, J. W., Kloke, J. D., & Sadek, M. (2017). A Monte Carlo study of REML and robust rank-based analyses for the random intercept mixed model. Communications in Statistics: Simulation and Computation, 48(3), 837-860.
  4. Azzalini, A. (1985). A Class of Distributions Which Includes the Normal Ones. Scandinavian Journal of Statistics, 12(2), 171-178.
  5. Azzalini, A, & Capitanio, A. (2014). The Skew-Normal and Related Families. Cambridge University Press.
  6. Azzalini, Adelchi. (2013). The skew-normal and related families. Cambridge University Press.
  7. Azzalini, Adelchi. (2014). The R sn Package: The skew-normal and skew-t distributions (1.0-0).
  8. Azzalini, Adelchi, & Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew tâ€distribution. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65(2), 367-389.
  9. Azzalini, Adelchi, & Genton, M. G. (2008). Robust likelihood methods based on the skewâ€t and related distributions. International Statistical Review, 76(1), 106-129.
  10. Basalamah, D. (2017). Statistical Inference for a New Class of Skew t Distribution and Its Related Properties. Bowling Green State University.
  11. Goldstein, H. (1995). Multilevel statistical models (second edi). Edward Arnold.
  12. Hájek, J., & Sidák, Z. (1967). Theory of rank tests. Academic Press.
  13. Hettmansperger, T. P., & McKean, J. W. (2010). Robust nonparametric statistical methods (second). CRC Press.
  14. Jaeckel, L. A. (1972). Estimating Regression Coefficients by Minimizing the Dispersion of the Residuals. The Annals of Mathematical Statistics, 43(5), 1449-1458.
  15. Kloke, J. D., & McKean, J. W. (2012). Rfit: Rank-based estimation for linear models. The R Journal, 4(2), 57-64.
  16. Kloke, John D., & Mckean, J. W. (2014). Nonparametric Statistical Methods Using R. Chapman and Hall/CRC.
  17. Kloke, John D, McKean, J. W., & Rashid, M. M. (2009). Rank-Based Estimation and Associated Inferences for Linear Models With Cluster Correlated Errors. Journal of the American Statistical Association, 104(485), 384-390.
  18. McKean, J. W., & Kloke, J. D. (2014). Efficient and adaptive rank-based fits for linear models with skew-normal errors. Journal of Statistical Distributions and Applications, 1(1), 1-18.