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The University of Southampton
Southampton Statistical Sciences Research Institute

S3RI Seminar - Professor Emeritus, Chihiro Hirotsu (Meisei University) Seminar

S3RI Seminar
Time:
14:00 - 15:00
Date:
14 June 2018
Venue:
University of Southampton Building 54, Seminar Room 8031 (8C) Highfield Campus Southampton SO17 1BJ

For more information regarding this seminar, please email Dr Helen Ogden at H.E.Ogden@soton.acuk .

Event details

The shape hypothesis (such as monotone) is essential in dose-response analysis where a rigid parametric model is usually difficult to assume. Then isotonic regression is the most well known approach. It has been, however, introduced rather intuitively and has no obvious optimality. Further the restricted maximum likelihood approach is computationally too complicated to extend to non-normal distributions, to other shape constraints and to two-way data. Instead our approach starts from a complete class lemma for the tests against a general restricted alternative. It suggests the use of the singly-, doubly- and triply-accumulated statistics for the monotone, convexity and sigmoidicity hypotheses, respectively. It should be stressed here that there is a close relationship between the shape and change-point hypotheses, which leads to a unifying approach to those two different topics in statistics. We propose the maximal contrast type statistics based on the accumulated statistics. The basic statistics are so simple and we have a very nice Markov property for an elegant and exact probability calculation not only for the normal distribution but also for the Poisson and multinomial distributions.

This approach is of so simple a structure that many of the procedures for one-way data can be extended in a systematic way to the analysis of two-way interaction, which is one of the central topics of the data science but receives much less attention than it deserves. There are variations that both or only one of the row or column categories have natural ordering. Indeed the analysis of the two-way interaction is a rich source of interesting theories and applications and the latter half of this talk is devoted to those interesting examples. The power of the proposed methods have been compared repeatedly and shown to be excellent.

 

Speaker information

Professor Emeritus Chihiro Hirotsu, Meisei University. Senior Researcher, Collaborative Research Center

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