A typical problem of interest is to compare the $k+1$ normal means under the tree order restriction $\theta_0\leq \theta_i$ for $i=1,\ldots,k$. In this paper, we propose new multiple comparisons procedures for testing of the tree order constraint. New test procedures along with the corresponding simultaneous confidence intervals are motivated by some new estimation methods which are constructed based on a random decision and the Bayesian approach. Also, these procedures are developed for twosided tree order alternatives. We compare the performance of the proposed methods with some existing test procedures, such as likelihood ratio test and some multiple comparisons tests for the tree order constraint. In some cases, the gains in power due to the proposed procedures are substantial. The results for two sided alternative are similar to the onesided hypotheses and new procedures perform well for almost every configuration. We illustrate the efficiency of the proposed methods by analyzing of the two bioassay numerical examples.
Dunnetttype test, likelihood ratio test, restricted maximum likelihood estimator, tree order constraint
Primary Language  English 

Subjects  Statistics and Probability 
Journal Section  Statistics 
Authors 

Publication Date  October 8, 2019 
Published in Issue  Year 2019, Volume 48, Issue 5 
Bibtex  @research article { hujms629933, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651477X}, eissn = {2651477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, pages = {1547  1559}, doi = {10.15672/hujms.481380}, title = {A random decision for testing of the homogeneity of normal means against the tree order alternative}, key = {cite}, author = {Momeni, Reza and Etminan, Javad and Sadegh, Mohammad Khanjari} } 
APA  Momeni, R. , Etminan, J. & Sadegh, M. K. (2019). A random decision for testing of the homogeneity of normal means against the tree order alternative . Hacettepe Journal of Mathematics and Statistics , 48 (5) , 15471559 . DOI: 10.15672/hujms.481380 
MLA  Momeni, R. , Etminan, J. , Sadegh, M. K. "A random decision for testing of the homogeneity of normal means against the tree order alternative" . Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 15471559 <https://dergipark.org.tr/en/pub/hujms/article/629933> 
Chicago  Momeni, R. , Etminan, J. , Sadegh, M. K. "A random decision for testing of the homogeneity of normal means against the tree order alternative". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 15471559 
RIS  TY  JOUR T1  A random decision for testing of the homogeneity of normal means against the tree order alternative AU  Reza Momeni , Javad Etminan , Mohammad Khanjari Sadegh Y1  2019 PY  2019 N1  doi: 10.15672/hujms.481380 DO  10.15672/hujms.481380 T2  Hacettepe Journal of Mathematics and Statistics JF  Journal JO  JOR SP  1547 EP  1559 VL  48 IS  5 SN  2651477X2651477X M3  doi: 10.15672/hujms.481380 UR  https://doi.org/10.15672/hujms.481380 Y2  2019 ER  
EndNote  %0 Hacettepe Journal of Mathematics and Statistics A random decision for testing of the homogeneity of normal means against the tree order alternative %A Reza Momeni , Javad Etminan , Mohammad Khanjari Sadegh %T A random decision for testing of the homogeneity of normal means against the tree order alternative %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651477X2651477X %V 48 %N 5 %R doi: 10.15672/hujms.481380 %U 10.15672/hujms.481380 
ISNAD  Momeni, Reza , Etminan, Javad , Sadegh, Mohammad Khanjari . "A random decision for testing of the homogeneity of normal means against the tree order alternative". Hacettepe Journal of Mathematics and Statistics 48 / 5 (October 2019): 15471559 . https://doi.org/10.15672/hujms.481380 
AMA  Momeni R. , Etminan J. , Sadegh M. K. A random decision for testing of the homogeneity of normal means against the tree order alternative. Hacettepe Journal of Mathematics and Statistics. 2019; 48(5): 15471559. 
Vancouver  Momeni R. , Etminan J. , Sadegh M. K. A random decision for testing of the homogeneity of normal means against the tree order alternative. Hacettepe Journal of Mathematics and Statistics. 2019; 48(5): 15471559. 
IEEE  R. Momeni , J. Etminan and M. K. Sadegh , "A random decision for testing of the homogeneity of normal means against the tree order alternative", Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 5, pp. 15471559, Oct. 2019, doi:10.15672/hujms.481380 