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Nonuniform Bounds for Nonparametric t-Tests

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  • Dufour, Jean-Marie
  • Hallin, Marc

Abstract

This paper gives simple nonuniform bounds on the tail areas of the permutation distribution of the usual Student's t -statistic when the observations are independent with symmetric distributions. As opposed to uniform bounds, nonuniform bounds depend on the observed sample. It is shown that the nonuniform bounds proposed are always tighter than uniform exponential bounds previously suggested. The use of the bounds to perform nonparametric t -tests is discussed and numerical examples are presented. Further, the bounds are extended to t -tests in the context of a simple linear regression.

Suggested Citation

  • Dufour, Jean-Marie & Hallin, Marc, 1991. "Nonuniform Bounds for Nonparametric t-Tests," Econometric Theory, Cambridge University Press, vol. 7(02), pages 253-263, June.
  • Handle: RePEc:cup:etheor:v:7:y:1991:i:02:p:253-263_00
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    1. Dufour, Jean-Marie & Farhat, Abdeljelil & Hallin, Marc, 2006. "Distribution-free bounds for serial correlation coefficients in heteroskedastic symmetric time series," Journal of Econometrics, Elsevier, vol. 130(1), pages 123-142, January.
    2. Renato Flôres & Ariane Szafarz, 1997. "Testing the Information Structure of Eastern European Markets: The Warsaw Stock Exchange," Economic Change and Restructuring, Springer, vol. 30(2), pages 91-105, May.
    3. Bryan Campbell & Eric Ghysels, 1997. "An Empirical Analysis of the Canadian Budget Process," Canadian Journal of Economics, Canadian Economics Association, vol. 30(3), pages 553-576, August.
    4. Dufour, Jean-Marie & Taamouti, Abderrahim, 2010. "Exact optimal inference in regression models under heteroskedasticity and non-normality of unknown form," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2532-2553, November.

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