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The Sensitivity of Chi-Squared Goodness-of-Fit Tests to the Partitioning of Data

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  • Gianna Boero
  • Jeremy Smith
  • Kenneth Wallis

Abstract

The power of Pearson's overall goodness-of-fit test and the components-of-chi-squared or “Pearson analog” tests of Anderson [Anderson, G. (1994). Simple tests of distributional form. J. Econometrics 62:265-276] to detect rejections due to shifts in location, scale, skewness and kurtosis is studied, as the number and position of the partition points is varied. Simulations are conducted for small and moderate sample sizes. It is found that smaller numbers of classes than are used in practice may be appropriate, and that the choice of non-equiprobable classes can result in substantial gains in power.

Suggested Citation

  • Gianna Boero & Jeremy Smith & Kenneth Wallis, 2005. "The Sensitivity of Chi-Squared Goodness-of-Fit Tests to the Partitioning of Data," Econometric Reviews, Taylor & Francis Journals, vol. 23(4), pages 341-370.
    • Handle: RePEc:taf:emetrv:v:23:y:2005:i:4:p:341-370
    DOI: 10.1081/ETC-200040782
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    References listed on IDEAS

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    1. Boero, Gianna & Marrocu, Emanuela, 2004. "The performance of SETAR models: a regime conditional evaluation of point, interval and density forecasts," International Journal of Forecasting, Elsevier, vol. 20(2), pages 305-320.
    2. Wallis, Kenneth F., 2003. "Chi-squared tests of interval and density forecasts, and the Bank of England's fan charts," International Journal of Forecasting, Elsevier, vol. 19(2), pages 165-175.
    3. repec:sae:niesru:v:167:y::i:1:p:106-112 is not listed on IDEAS
    4. Marrocu, Emanuela & Gianna Boero, 2003. "The Performance of SETAR models by Regime: A Conditional Evaluation of Interval and Density Forecasts," Royal Economic Society Annual Conference 2003 147, Royal Economic Society.
    5. Kenneth F. Wallis, 1999. "Asymmetric density forecasts of inflation and the Bank of England's fan chart," National Institute Economic Review, National Institute of Economic and Social Research, vol. 167(1), pages 106-112, January.
    6. Benoit Mandelbrot, 1963. "New Methods in Statistical Economics," Journal of Political Economy, University of Chicago Press, vol. 71(5), pages 421-421.
    7. Anderson, Gordon, 1994. "Simple tests of distributional form," Journal of Econometrics, Elsevier, vol. 62(2), pages 265-276, June.
    8. Boero, Gianna & Smith, Jeremy & Wallis, Kenneth F., 2004. "Decompositions of Pearson's chi-squared test," Journal of Econometrics, Elsevier, vol. 123(1), pages 189-193, November.
    9. Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, vol. 64(5), pages 1183-1193, September.
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    Cited by:

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    2. Oller, Lars-Erik & Teterukovsky, Alex, 2007. "Quantifying the quality of macroeconomic variables," International Journal of Forecasting, Elsevier, vol. 23(2), pages 205-217.
    3. Gordon Anderson, 2008. "The empirical assessment of multidimensional welfare, inequality and poverty: Sample weighted multivariate generalizations of the Kolmogorov–Smirnov two sample tests for stochastic dominance," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 6(1), pages 73-87, March.
    4. Bontemps, Christian, 2014. "Simple moment-based tests for value-at-risk models and discrete distribution," TSE Working Papers 14-535, Toulouse School of Economics (TSE).
    5. Hasebe, Takuya & Vijverberg, Wim P., 2012. "A Flexible Sample Selection Model: A GTL-Copula Approach," IZA Discussion Papers 7003, Institute of Labor Economics (IZA).
    6. Bontemps, Christian, 2013. "Moment-Based Tests for Discrete Distributions," IDEI Working Papers 772, Institut d'Économie Industrielle (IDEI), Toulouse, revised Oct 2014.

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    More about this item

    Keywords

    Pearson's goodness-of-fit test; Component tests; Monte Carlo; Number of classes; Partitions;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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