IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v196y2023ics0047259x23000234.html
   My bibliography  Save this article

Testing against ordered alternatives in a two-way model without interaction under heteroscedasticity

Author

Listed:
  • Mondal, Anjana
  • Sattler, Paavo
  • Kumar, Somesh

Abstract

In this paper, we consider tests for homogeneity of row effects against ordered alternatives in a randomized block design without interaction effects. Error variances in all cells are assumed to be heterogeneous and data are unbalanced. The likelihood ratio test (LRT) and two heuristic tests named Min-T and Max-T are proposed. Numerical procedures to find solutions of likelihood equations under null hypothesis space and full parameter space are developed. The existence and uniqueness of the solutions and the convergence of the algorithm are established. Parametric bootstrap (PB) is used to evaluate critical points and to estimate sizes and powers of these tests. Asymptotic distributions of the heuristic test statistics are derived and tests are proposed based on these also. Asymptotic accuracy of bootstrap procedures is established in all cases. Using Max-T test we have derived simultaneous confidence intervals for successive pair-wise differences of row-effects. An extensive simulation study shows that all the proposed PB tests maintain a preassigned type I error 0.05. Power comparison shows that LRT achieves more power values than all the other tests. However, Min-T and Max-T tests are easy to implement and take considerably less time as these do not need the evaluation of maximum likelihood estimators (MLEs). The robustness of all tests is also studied and it is seen that LRT is not robust for some skewed distributions. However, heuristic tests are robust in all cases. This is also one advantage of using Min-T and Max-T tests.

Suggested Citation

  • Mondal, Anjana & Sattler, Paavo & Kumar, Somesh, 2023. "Testing against ordered alternatives in a two-way model without interaction under heteroscedasticity," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    • Handle: RePEc:eee:jmvana:v:196:y:2023:i:c:s0047259x23000234
    DOI: 10.1016/j.jmva.2023.105177
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X23000234
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2023.105177?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Shi, N. Z., 1994. "Maximum Likelihood Estimation of Means and Variances from Normal Populations Under Simultaneous Order Restrictions," Journal of Multivariate Analysis, Elsevier, vol. 50(2), pages 282-293, August.
    2. Markus Pauly & Edgar Brunner & Frank Konietschke, 2015. "Asymptotic permutation tests in general factorial designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 461-473, March.
    3. Shi, Ning-Zhong & Jiang, Hua, 1998. "Maximum Likelihood Estimation of Isotonic Normal Means with Unknown Variances," Journal of Multivariate Analysis, Elsevier, vol. 64(2), pages 183-195, February.
    4. Bretz, Frank, 2006. "An extension of the Williams trend test to general unbalanced linear models," Computational Statistics & Data Analysis, Elsevier, vol. 50(7), pages 1735-1748, April.
    5. OrI Davidov & Konstantinos Fokianos & George Iliopoulos, 2014. "Semiparametric Inference for the Two-way Layout Under Order Restrictions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 622-638, September.
    6. Xu, Li-Wen & Yang, Fang-Qin & Abula, Aji’erguli & Qin, Shuang, 2013. "A parametric bootstrap approach for two-way ANOVA in presence of possible interactions with unequal variances," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 172-180.
    7. Konietschke, Frank & Bathke, Arne C. & Harrar, Solomon W. & Pauly, Markus, 2015. "Parametric and nonparametric bootstrap methods for general MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 291-301.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Friedrich, Sarah & Pauly, Markus, 2018. "MATS: Inference for potentially singular and heteroscedastic MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 166-179.
    2. Smaga, Łukasz, 2015. "Wald-type statistics using {2}-inverses for hypothesis testing in general factorial designs," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 215-220.
    3. Dickhaus, Thorsten & Sirotko-Sibirskaya, Natalia, 2019. "Simultaneous statistical inference in dynamic factor models: Chi-square approximation and model-based bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 30-46.
    4. H. V. Kulkarni & S. M. Patil, 2021. "Uniformly implementable small sample integrated likelihood ratio test for one-way and two-way ANOVA under heteroscedasticity and normality," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(2), pages 273-305, June.
    5. Friedrich, Sarah & Brunner, Edgar & Pauly, Markus, 2017. "Permuting longitudinal data in spite of the dependencies," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 255-265.
    6. Jamshidian, Mortaza, 2004. "On algorithms for restricted maximum likelihood estimation," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 137-157, March.
    7. Burim Ramosaj & Markus Pauly, 2019. "Predicting missing values: a comparative study on non-parametric approaches for imputation," Computational Statistics, Springer, vol. 34(4), pages 1741-1764, December.
    8. Hoferkamp, Carol & Das Peddada, Shyamal, 2002. "Parameter Estimation in Linear Models with Heteroscedastic Variances Subject to Order Restrictions," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 65-87, July.
    9. Milica Maricic & Jose A. Egea & Veljko Jeremic, 2019. "A Hybrid Enhanced Scatter Search—Composite I-Distance Indicator (eSS-CIDI) Optimization Approach for Determining Weights Within Composite Indicators," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 144(2), pages 497-537, July.
    10. Marc Ditzhaus & Roland Fried & Markus Pauly, 2021. "QANOVA: quantile-based permutation methods for general factorial designs," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 960-979, December.
    11. Markus Pauly & Maria Umlauft & Ali Ünlü, 2018. "Resampling-Based Inference Methods for Comparing Two Coefficients Alpha," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 203-222, March.
    12. Bogomolov, Marina & Davidov, Ori, 2019. "Order restricted univariate and multivariate inference with adjustment for covariates in partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 20-27.
    13. Konietschke, Frank & Bathke, Arne C. & Harrar, Solomon W. & Pauly, Markus, 2015. "Parametric and nonparametric bootstrap methods for general MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 291-301.
    14. Shi, Ning-Zhong & Zheng, Shu-Rong & Guo, Jianhua, 2005. "The restricted EM algorithm under inequality restrictions on the parameters," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 53-76, January.
    15. Shi, Ning-Zhong & Jiang, Hua, 1998. "Maximum Likelihood Estimation of Isotonic Normal Means with Unknown Variances," Journal of Multivariate Analysis, Elsevier, vol. 64(2), pages 183-195, February.
    16. Marinho Bertanha & Eunyi Chung, 2023. "Permutation Tests at Nonparametric Rates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(544), pages 2833-2846, October.
    17. Xu, Li-Wen, 2015. "Parametric bootstrap approaches for two-way MANOVA with unequal cell sizes and unequal cell covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 291-303.
    18. Hasler Mario, 2013. "Multiple Contrasts for Repeated Measures," The International Journal of Biostatistics, De Gruyter, vol. 9(1), pages 1-13, July.
    19. Mario Hasler, 2016. "Heteroscedasticity: multiple degrees of freedom vs. sandwich estimation," Statistical Papers, Springer, vol. 57(1), pages 55-68, March.
    20. Hothorn Ludwig A & Sill Martin & Schaarschmidt Frank, 2010. "Evaluation of Incidence Rates in Pre-Clinical Studies Using a Williams-Type Procedure," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-19, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:196:y:2023:i:c:s0047259x23000234. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.