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The split-up algorithm: a fast symbolic method for computing p-values of distribution-free statistics

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  • Mark van de Wiel

    (Eindhoven University of Technology)

Abstract

Summary Many distribution-free statistics have the drawback that computing exact p-values under the null hypothesis is an intensive task. When the sample sizes are small or the number of ties is large, approximations are often unsatisfactory. Moreover, tables of exact critical values are not available for conditional rank statistics (ties, censoring), for rank statistics with arbitrary regression constants, or for permutation test statistics. In those cases, it is important to have a fast algorithm for computing exact p-values. We present a new algorithm and apply it to a large class of distribution-free one-sample, two-sample and serial statistics. The algorithm is based on splitting the probability generating function of the test statistic into two parts. We compare the speed of this “split-up algorithm” to that of existing procedures and we conclude that our new algorithm is faster in many cases.

Suggested Citation

  • Mark van de Wiel, 2001. "The split-up algorithm: a fast symbolic method for computing p-values of distribution-free statistics," Computational Statistics, Springer, vol. 16(4), pages 519-538, December.
    • Handle: RePEc:spr:compst:v:16:y:2001:i:4:d:10.1007_s180-001-8328-6
    DOI: 10.1007/s180-001-8328-6
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    References listed on IDEAS

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    1. Hallin, Marc & Puri, Madan L., 1991. "Time series analysis via rank order theory: Signed-rank tests for ARMA models," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 1-29, October.
    2. Marc Hallin & Madan Lal Puri, 1988. "Optimal rank-based procedures for time series analysis: testing an ARMA model against other ARMA models," ULB Institutional Repository 2013/2013, ULB -- Universite Libre de Bruxelles.
    3. Marc Hallin & Guy Melard, 1988. "Rank-based tests for randomness against first-order serial dependence," ULB Institutional Repository 2013/2015, ULB -- Universite Libre de Bruxelles.
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    1. repec:jss:jstsof:28:i08 is not listed on IDEAS
    2. Beninel, Farid & Grelaud, Gerard, 2007. "Exact algorithms for computing p-values of statistics-linear combination of 3-nomial variables," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 737-749, October.

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