Changepoint Analysis as a Method for Isotonic Inference |
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Authors: | CHIHIRO HIROTSU & KOHEI MARUMO |
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Institution: | Meisei University, Japan,;Nippon-Ginko, Japan |
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Abstract: | Concavity and sigmoidicity hypotheses are developed as a natural extension of the simple ordered hypothesis in normal means. Those hypotheses give reasonable shape constraints for obtaining a smooth response curve in the non-parametric inputoutput analysis. The slope change and inflection point models are introduced correspondingly as the corners of the polyhedral cones defined by those isotonic hypotheses. Then a maximal contrast type test is derived systematically as the likelihood ratio test for each of those changepoint hypotheses. The test is also justified for the original isotonic hypothesis by a complete class lemma. The component variables of the resulting test statistic have second or third order Markov property which, together with an appropriate non-linear transformation, leads to an exact and very efficient algorithm for the probability calculation. Some considerations on the power of the test are given showing this to be a very promising way of approaching to the isotonic inference. |
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Keywords: | concavity extended max t test inflection maximin linear test non-parametric doseresponse analysis Markov property sigmoidicity slope change |
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