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Frame theory in directional statistics

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  • Ehler, Martin
  • Galanis, Jennifer

Abstract

Distinguishing between uniform and non-uniform sample distributions is a common problem in directional data analysis; however for many tests, non-uniform distributions exist that fail uniformity rejection. To predict these distributions, we merge directional statistics with frame theory and find that probabilistic tight frames yield non-uniform distributions that minimize directional potentials, leading to failure of uniformity rejection for the Bingham test. Finally, we apply our results to model patterns found in granular rod experiments.

Suggested Citation

  • Ehler, Martin & Galanis, Jennifer, 2011. "Frame theory in directional statistics," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1046-1051, August.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1046-1051
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    References listed on IDEAS

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    1. Rueda, Cristina & Fernández, Miguel A. & Peddada, Shyamal Das, 2009. "Estimation of Parameters Subject to Order Restrictions on a Circle With Application to Estimation of Phase Angles of Cell Cycle Genes," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 338-347.
    2. Kanti V. Mardia & Charles C. Taylor & Ganesh K. Subramaniam, 2007. "Protein Bioinformatics and Mixtures of Bivariate von Mises Distributions for Angular Data," Biometrics, The International Biometric Society, vol. 63(2), pages 505-512, June.
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    1. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    2. Martin Ehler, 2015. "Preconditioning Filter Bank Decomposition Using Structured Normalized Tight Frames," Journal of Applied Mathematics, John Wiley & Sons, vol. 2015(1).
    3. Tobias Springer & Katja Ickstadt & Joachim Stöckler, 2011. "Frame potential minimization for clustering short time series," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 5(4), pages 341-355, December.

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