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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.)

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Bibliographic Info

Paper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 1201.

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Length: 28 pages
Date of creation: 12 Jan 2012
Date of revision:
Handle: RePEc:vic:vicewp:1201

Note: ISSN 1485-6441
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Keywords: Distributions on the circle; Goodness-of-fit; Watson’s 2N U; Discrete data; Benford’s Law;

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  1. David E. Giles, 2005. "Benford’s Law and Naturally Occurring Prices in Certain ebaY Auctions," Econometrics Working Papers 0505, Department of Economics, University of Victoria.
  2. 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.
  3. 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.
  4. Canessa, Enrique, 2003. "Theory of analogous force on number sets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 328(1), pages 44-52.
  5. 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.
  6. 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.
  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. Ocean Fan Lu & David E. A. Giles, 2006. "Benford's Law and Psychological Barriers in Certain eBay Auctions," Econometrics Working Papers 0606, Department of Economics, University of Victoria.
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