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Contingency tables with ordered categories frequently arise in
medical,biological and social science which a subject is
classified into several categories.For example,tow doctors
diagnose a group of patients for some disease and the patients are
classified into four levels:serious,probable,doubtful,and
definitely not.If the two doctors has similar knowledge about
this kind of disease,they will have the same possibility to
classify patients into the four levels,which is usually called
the marginal homogeneity.If one has more knowledge about the
disease,there will have some trend between them,for example,
maybe the one with more knowledge classifies the patients into
more likely at least serious,probable,doubtful respectively than
the other,this trend is often called stochastically ordered
marginal.A lot of authors have considered this kind of problem,
such as Agresti(1983,Biometrics,39,505-510),Becker,(1990,
JRSSB,369-378),Dardanoni and Forcina(1998,JASA,93,1112-1123).
In[1],by introducing the Kullback-Leibler measurement,we study
the above problem and a optimal solution is defined.A simple
algorithm to compute the optimal solution for stochastically
ordered marginal models is proposed,which generalizes the result
given by lreland,Ku,and Kullback(1969,JASA,64,1323-1341).
Also for testing marginal homogeneity against stochastically
ordered marginal,a test based on Kullback-Leibler information is
given and prove that its asymptotic distribution under marginal
homogeneity is the chi-bar square distribution.In[2],we study
the relationships between I-projection onto isotonic cones and the
MLE of parameters for the multinomial distribution.We demonstrate
they are same when the model is log-linear and the
parameters in the model are restricted by some ordered
restrictions.Meantime,an algorithm is proposed.
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