214
Views
5
CrossRef citations to date
0
Altmetric
Original Articles

Bootstrapping analogs of the one way MANOVA test

&
Pages 5546-5558 | Received 05 Mar 2018, Accepted 16 Aug 2018, Published online: 23 Oct 2018

References

  • Anderson, M. 2001. A new method for non-parametric multivariate analysis of variance. Austral Ecology 26 (1):32–46. doi:10.1111/j.1442-9993.2001.01070.pp.x.
  • Bathke, A. C., S. Friedrich, M. Pauly, F. Konietschke, W. Staffen, N. Strobl, and Y. Höller. 2018. Testing mean differences among groups: Multivariate and repeated measures analysis with minimal assumptions. Multivariate Behavioral Research 53 (3):348–59. doi:10.1080/00273171.2018.1446320.
  • Bathke, A. C., and S. W. Harrar. 2008. Nonparametric methods in multivariate factorial designs for large number of factor levels. Journal of Statistical Planning and Inference 138 (3):588–610. doi:10.1016/j.jspi.2006.11.004.
  • Bathke, A. C., S. W. Harrar, and M. R. Ahmad. 2009. Some contributions to the analysis of multivariate data. Biometrical Journal. Biometrische Zeitschrift 51 (2):285–303. doi:10.1002/bimj.200800196.
  • Bathke, A. C., S. W. Harrar, and L. V. Madden. 2008. How to compare small multivariate samples using nonparametric tests. Computational Statistics and Data Analysis 52 (11):4951–65. doi:10.1016/j.csda.2008.04.006.
  • Bickel, P. J., and J.-J. Ren. 2001. The bootstrap in hypothesis testing. In State of the art in probability and statistics: Festschrift for William R. van Zwet, M. de Gunst, C. Klaassen, and A. van der Vaart ed. 91–112. Hayward, CA: The Institute of Mathematical Statistics.
  • Clarke, B. R. 1986. Nonsmooth analysis and Fréchet differentiability of M functionals. Probability Theory and Related Fields 73 (2):197–209. doi:10.1007/BF00339936.
  • Clarke, B. R. 2000. A review of differentiability in relation to robustness with an application to seismic data analysis. Proceedings of the Indian National Science Academy A 66:467–82.
  • Cornwell, C., and W. N. Trumbull. 1994. Estimating the economic model of crime with panel data. Review of Economics and Statistics 76 (2):360–6. doi:10.2307/2109893.
  • Ellis, A. R., W. W. Burchett, S. W. Harrar, and A. C. Bathke. 2017. Nonparametric inference for multivariate data: The R package NPMV. Journal of Statistical Software 76 (4):1–18. doi:10.18637/jss.v076.i04.
  • Fernholtz, L. T. 1983. Von mises calculus for statistical functionals. New York: Springer.
  • Finch, H., and B. French. 2013. A “Monte Carlo” comparison of robust MANOVA test statistics. Journal of Modern Applied Statistical Methods 12 (2):35–81. doi:10.22237/jmasm/1383278580.
  • Friedrich, S., F. Konietschke, and M. Pauly. 2016. MANOVA.RM: Analysis of multivariate data and repeated measures designs. R package version 2.1. https://CRAN.R-project.org/package=MANOVA.RM.
  • Fujikoshi, Y. 2002. Asymptotic expansions for the distributions of multivariate basic statistics and one-way MANOVA tests under nonnormality. Journal of Statistical Planning and Inference 108 (1–2):263–82. doi:10.1016/S0378-3758(02)00313-0.
  • Ghosh, S., and A. M. Polanski. 2014. Smoothed and iterated bootstrap confidence regions for parameter vectors. Journal of Multivariate Analysis 132:171–82. doi:10.1016/j.jmva.2014.08.003.
  • Gill, R. D. 1989. Non- and semi-parametric maximum likelihood estimators and the von Mises method, part 1. Scandinavian Journal of Statistics 16:97–128.
  • Girön, F., and C. del Castillo. 2010. The multivariate Behrens-Fisher distribution. Journal of Multivariate Analysis 101 (9):2091–102. doi:10.1016/j.jmva.2010.04.008.
  • Harrar, S. W., and A. C. Bathke. 2008a. A nonparametric version of the Bartlett-Nanda-Pillai Multivariate test. Asymptotics, approximations, and applications. American Journal of Mathematical and Management Sciences 28 (3–4):309–35. doi:10.1080/01966324.2008.10737731.
  • Harrar, S. W., and A. C. Bathke. 2008b. Nonparametric methods for unbalanced multivariate data and many factor levels. Journal of Multivariate Analysis 99 (8):1635–64. doi:10.1016/j.jmva.2008.01.005.
  • Kakizawa, Y. 2009. Third-order power comparisons for a class of tests for multivariate linear hypothesis under general distributions. Journal of Multivariate Analysis 100 (3):473–96. doi:10.1016/j.jmva.2008.06.002.
  • Kawasaki, T., and T. Seo. 2015. A two sample test for mean vectors with unequal covariance matrices. Communications in Statistics: Simulation and Computation 44 (7):1850–66. doi:10.1080/03610918.2013.824587.
  • Konietschke, F., A. C. Bathke, S. W. Harrar, and M. Pauly. 2015. Parametric and nonparametric bootstrap methods for general MANOVA. Journal of Multivariate Analysis 140:291–301. doi:10.1016/j.jmva.2015.05.001.
  • Krishnamoorthy, K., and F. Lu. 2010. A parametric bootstrap solution to the MANOVA under heteroscedasticity. Journal of Statistical Computation and Simulation 80 (8):873–87. doi:10.1080/00949650902822564.
  • Krishnamoorthy, K., and J. Yu. 2004. Modified Nel and Van der Merwe test for the multivariate Behrens-Fisher problem. Statistics & Probability Letters 66 (2):161–9. doi:10.1016/j.spl.2003.10.012.
  • Liu, C., A. C. Bathke, and S. W. Harrar. 2011. A nonparametric version of Wilks’ lambda-asymptotic results and small sample approximations. Statistics & Probability Letters 81 (10):1502–6. doi:10.1016/j.spl.2011.04.012.
  • Machado, J. A. F., and P. Parente. 2005. Bootstrap estimation of covariance matrices via the percentile method. The Econometrics Journal 8 (1):70–8. doi:10.1111/j.1368-423X.2005.00152.x.
  • Nel, D. G., and C. A. Van Der Merwe. 1986. A solution to the multivariate Behrens-Fisher problem. Communications in Statistics: Theory and Methods 15 (12):3719–35. doi:10.1080/03610928608829342.
  • Olive, D. J. 2017a. Robust multivariate analysis. New York: Springer.
  • Olive, D. J. 2017b. Bootstrapping hypothesis tests and confidence regions. Unpublished Manuscript with the bootstrap material from Olive (2017a). http://lagrange.math.siu.eduOlive/ppvselboot.pdf.
  • Olive, D. J. 2018. Applications of hyperellipsoidal prediction regions. Statistical Papers 59 (3):913–31
  • Pelawa Watagoda, L. C. R., and D. J. Olive. 2018. Bootstrapping multiple linear regression after variable selection (Unpublished manuscript). (http://lagrange.math.siu.edu/Olive/ppboottest.pdf).
  • Pesarin, F., and L. Salmaso. 2012. A review and some new results on permutation testing for multivariate problems. Statistics and Computing 22 (2):639–46. doi:10.1007/s11222-011-9261-0.
  • R Core Team. 2016. R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing. www.R-project.org.
  • Ren, J.-J. 1991. On Hadamard differentiability of extended statistical functional. Journal of Multivariate Analysis 39 (1):30–43. doi:10.1016/0047-259X(91)90003-K.
  • Ren, J.-J., and P. K. Sen. 1995. Hadamard differentiability on D[0,1]p. Journal of Multivariate Analysis 55 (1):14–28. doi:10.1006/jmva.1995.1064.
  • Rupasinghe Arachchige Don, H. S. 2017. Bootstrapping analogs of the one way MANOVA test. Ph.D. Thesis, Southern Illinois University, USA. http://lagrange.math.siu.edu/Olive/shasthikaphd.pdf.
  • Rupasinghe Arachchige Don, H. S., and L. C. R. Pelawa Watagoda. 2017. Bootstrapping analogs of the two sample Hotelling’s T2 test. Communications and Statistics: Theory and Methods 47 (9):2172–82. doi:10.1080/03610926.2017.1337146.
  • Todorov, V., and P. Filzmoser. 2010. Robust statistics for the one-way MAVOVA. Computational Statistics & Data Analysis 54 (1):37–48. doi:10.1016/j.csda.2009.08.015.
  • Vallejo, G., and M. Ato. 2012. Robust tests for multivariate factorial designs under heteroscedasticity. Behavior Research Methods 44 (2):471–89. doi:10.3758/s13428-011-0152-2.
  • Van Aelst, S., and G. Willems. 2011. Robust and efficient one-way MANOVA tests. Journal of the American Statistical Association 106 (494):706–18. doi:10.1198/jasa.2011.tm09748.
  • Van Aelst, S., and G. Willems. 2013. Fast and robust bootstrap for multivariate inference: The R package FRB. Journal of Statistical Software 53 (3):1–32. doi:10.18637/jss.v053.i03.
  • Wilcox, R. R. 1995. Simulation results on solutions to the multivariate “Behrens-Fisher” problem via trimmed means. The Statistician 44 (2):213–25. doi:10.2307/2348445.
  • Zhang, J. T. 2012. An approximate Hotelling T2-test for heteroscedastic one-way MANOVA. Open Journal of Statistics 02 (01):1–11. doi:10.4236/ojs.2012.21001.
  • Zhang, J. T., and X. Liu. 2013. A modified Bartlett test for heteroscedastic one-way MANOVA. Metrika 76 (1):135–52. doi:10.1007/s00184-011-0379-z.

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.