Changepoint Analysis as a Method for Isotonic Inference

Chihiro Hirotsu and Kohei Marumo

Scandinavian Journal of Statistics, 2002, vol. 29, issue 1, 125-138

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 input–output 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.

Date: 2002
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