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Exact Asymptotic Goodness-of-Fit Testing For Discrete Circular Data, With Applications

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Abstract

We show that the full asymptotic null distribution for Watson’s 2N U statistic, modified for discrete data, can be computed simply and exactly by standard methods. Previous approximate quantiles for the uniform multinomial case are found to be accurate. More extensive quantiles are presented for this distribution, as well as for the beta-binomial distribution and for the distributions associated with “Benford’s Laws”. A simulation experiment compares the power of the modified 2N U test with that of Kuiper’s VN test. In addition, four illustrative empirical applications are provided. In addition, four illustrative empirical applications are provided to illustrate the usefulness of the 2N U test. (This paper supercedes EWP0607.)

Suggested Citation

  • David E. Giles, 2012. "Exact Asymptotic Goodness-of-Fit Testing For Discrete Circular Data, With Applications," Econometrics Working Papers 1201, Department of Economics, University of Victoria.
  • Handle: RePEc:vic:vicewp:1201
    Note: ISSN 1485-6441
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    References listed on IDEAS

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    1. Shao, Lijing & Ma, Bo-Qiang, 2010. "The significant digit law in statistical physics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3109-3116.
    2. De Ceuster, Marc J. K. & Dhaene, Geert & Schatteman, Tom, 1998. "On the hypothesis of psychological barriers in stock markets and Benford's Law," Journal of Empirical Finance, Elsevier, vol. 5(3), pages 263-279, September.
    3. Hunt, Daniel L. & Cheng, Cheng & Pounds, Stanley, 2009. "The beta-binomial distribution for estimating the number of false rejections in microarray gene expression studies," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1688-1700, March.
    4. Ocean Fan Lu & David Giles, 2010. "Benford's Law and psychological barriers in certain eBay auctions," Applied Economics Letters, Taylor & Francis Journals, vol. 17(10), pages 1005-1008.
    5. David Giles, 2007. "Benford's law and naturally occurring prices in certain ebaY auctions," Applied Economics Letters, Taylor & Francis Journals, vol. 14(3), pages 157-161.
    6. Balanzario, Eugenio P. & Sánchez-Ortiz, Jorge, 2010. "Sufficient conditions for Benford's law," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1713-1719, December.
    7. George Judge & Laura Schechter, 2009. "Detecting Problems in Survey Data Using Benford’s Law," Journal of Human Resources, University of Wisconsin Press, vol. 44(1).
    8. Canessa, Enrique, 2003. "Theory of analogous force on number sets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 328(1), pages 44-52.
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    More about this item

    Keywords

    Distributions on the circle; Goodness-of-fit; Watson’s 2N U; Discrete data; Benford’s Law;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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