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A unifying approach to the shape and change-point hypotheses in the discrete univariate exponential family

Author

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  • Hirotsu, Chihiro
  • Yamamoto, Shoichi
  • Tsuruta, Harukazu

Abstract

A unifying approach to the shape and change-point hypotheses is extended generally to a discrete univariate exponential family. The maximal contrast type tests are newly proposed for the convexity and sigmoidicity hypotheses based on the complete class lemma of tests for the restricted alternatives. Those tests are also efficient score tests for the slope change-point and inflection point models, respectively. For each of those tests the successive component statistics are the doubly- and triply-accumulated statistics. They have nice Markov properties for the exact and efficient recursion formulae for calculating the p-value. Further the sum of squares of the component statistics are developed as the cumulative chi-squared statistics for the directional goodness-of-fit tests of the dose–response model. Therefore the interesting applications will be in monitoring of spontaneous reporting of the adverse drug events and the directional goodness-of-fit tests.

Suggested Citation

  • Hirotsu, Chihiro & Yamamoto, Shoichi & Tsuruta, Harukazu, 2016. "A unifying approach to the shape and change-point hypotheses in the discrete univariate exponential family," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 33-46.
    • Handle: RePEc:eee:csdana:v:97:y:2016:i:c:p:33-46
    DOI: 10.1016/j.csda.2015.11.012
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    References listed on IDEAS

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    1. Hirotsu, C., 2009. "Clustering rows and/or columns of a two-way contingency table and a related distribution theory," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4508-4515, October.
    2. Chihiro Hirotsu & Eri Ohta & Nobuyoshi Hirose & Kenichiro Shimizu, 2003. "Profile Analysis of 24-Hours Measurements of Blood Pressure," Biometrics, The International Biometric Society, vol. 59(4), pages 907-915, December.
    3. Chihiro Hirotsu & Kohei Marumo, 2002. "Changepoint Analysis as a Method for Isotonic Inference," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 125-138, March.
    4. Chihiro Hirotsu & Satoshi Aoki & Toshiya Inada & Yoshie Kitao, 2001. "An Exact Test for the Association Between the Disease and Alleles at Highly Polymorphic Loci with Particular Interest in the Haplotype Analysis," Biometrics, The International Biometric Society, vol. 57(3), pages 769-778, September.
    5. Hirotsu, Chihiro & Srivastava, Muni S., 2000. "Simultaneous confidence intervals based on one-sided max t test," Statistics & Probability Letters, Elsevier, vol. 49(1), pages 25-37, August.
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