• Journal of the Korean Statistical Society
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• v.21 no.2
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• pp.201-207
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• 1992

The algorithm for obtaining the isotonic regression in simple tree order, the most basic and simplest model next to the simple order, is considered. We propose to call it "Pool-the-Maximum-Violators" algorithm (PMVA) in conjunction with the "Pool-Adjacent-Violators" algorithm (PAVA) in the simple order. The dual problem of obtaining the isotonic regression in simple tree order is our main concern. An intuitively appealing relation between the primal and the dual problems is demonstrated. The interesting difference is that in simple order the required number of pooling is at least the number of initial violating pairs and any path leads to the solution, whereas in the simple tree order it is at most the number of initial violators and there is only one advisable path although there may be some others leading to the same solution.o the same solution.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.699-709
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• 2000

The constrained maximum likelihood estimation of the number of trials in several binomial populations under order restriction, such as simple order, is discussed. The estimation procedure is based on, so called, pool adjacent violators algorithm. Three handy estimators are given and their performances are compared using an artificial example.