Yıl 2019, Cilt 48 , Sayı 5, Sayfalar 1547 - 1559 2019-10-08

A random decision for testing of the homogeneity of normal means against the tree order alternative

Reza Momeni [1] , Javad Etminan [2] , Mohammad Khanjari Sadegh [3]


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 two-sided 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 one-sided 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.
Dunnett-type test, likelihood ratio test, restricted maximum likelihood estimator, tree order constraint
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Birincil Dil en
Konular İstatistik ve Olasılık
Bölüm İstatistik
Yazarlar

Orcid: 0000-0001-9879-9946
Yazar: Reza Momeni (Sorumlu Yazar)

Orcid: 0000-0003-0069-5407
Yazar: Javad Etminan

Orcid: 0000-0002-2647-5632
Yazar: Mohammad Khanjari Sadegh

Tarihler

Yayımlanma Tarihi : 8 Ekim 2019

Bibtex @araştırma makalesi { hujms629933, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2019}, volume = {48}, pages = {1547 - 1559}, doi = {}, 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 . (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) , 1547-1559 . Retrieved from https://dergipark.org.tr/tr/pub/hujms/issue/49321/629933
MLA Momeni, R , Etminan, J , Sadegh, M . "A random decision for testing of the homogeneity of normal means against the tree order alternative". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1547-1559 <https://dergipark.org.tr/tr/pub/hujms/issue/49321/629933>
Chicago Momeni, R , Etminan, J , Sadegh, M . "A random decision for testing of the homogeneity of normal means against the tree order alternative". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1547-1559
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 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1547 EP - 1559 VL - 48 IS - 5 SN - 2651-477X-2651-477X M3 - UR - 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 2651-477X-2651-477X %V 48 %N 5 %R %U
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 (Ekim 2019): 1547-1559 .
AMA Momeni R , Etminan J , Sadegh M . 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): 1547-1559.
Vancouver Momeni R , Etminan J , Sadegh M . 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): 1559-1547.