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A Trinomial Test for Paired Data When There are Many Ties


  • Guorui Bian

    (Department of Statistics, East China Normal University)

  • Michael McAleer

    (Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam and Tinbergen Institute and Center for International Research on the Japanese Economy (CIRJE), Faculty of Economics, University of Tokyo)

  • Wing-Keung Wong

    (Department of Economics and Institute for Computational Mathematics, Hong Kong Baptist University)


This paper develops a new test, the trinomial test, for pairwise ordinal data samples to improve the power of the sign test by modifying its treatment of zero diRerences between observations, thereby increasing the use of sample information. Simulations demonstrate the power superiority of the proposed trinomial test statis- tic over the sign test in small samples in the presence of tie observations. We also show that the proposed trinomial test has substantially higher power than the sign test in large samples and also in the presence of tie observations, as the sign test ignores information from observations resulting in ties.

Suggested Citation

  • Guorui Bian & Michael McAleer & Wing-Keung Wong, 2009. "A Trinomial Test for Paired Data When There are Many Ties," CIRJE F-Series CIRJE-F-662, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2009cf662

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    References listed on IDEAS

    1. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    2. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    3. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
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    Cited by:

    1. Chang, C-L. & McAleer, M.J. & Wong, W.-K., 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," Econometric Institute Research Papers EI 2018-08, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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