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On optimal tests for isotropy against the symmetric wrapped stable-circular uniform mixture family

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  • Ashis Sengupta
  • Chandranath Pal

Abstract

The family of Symmetric Wrapped Stable (SWS) distributions can be widely used for modelling circular data. Mixtures of Circular Uniform (CU) with the former also have applications as a larger family of circular distributions to incorporate possible outliers. Restricting ourselves to such a mixture, we derive the locally most powerful invariant (LMPI) test for the hypothesis of isotropy or randomness of directions-expressed in terms of the null value of the mixing proportion, p, in the model. Global monotonicity of the power function of the test is established. The test is also consistent. Power values of the test for some selected parameter combinations, obtained through simulation reveal quite encouraging performances even for moderate sample sizes. The P 3 approach (SenGupta, 1991; Pal & SenGupta, 2000) for unknown p and rho and the non-regular case of unknown a, the index parameter, are also discussed. A real-life example is presented to illustrate the inadequacy of the circular normal distribution as a circular model. This example is also used to demonstrate the applications of the LMPI test, optimal P 3 test and a Daviesmotivated test (Davies, 1977, 1987). Finally, a goodness-of-fit test performed on the data establishes the plausibility of the above SWS-CU mixture model for real-life problems encountered in practical situations.

Suggested Citation

  • Ashis Sengupta & Chandranath Pal, 2001. "On optimal tests for isotropy against the symmetric wrapped stable-circular uniform mixture family," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(1), pages 129-143.
    • Handle: RePEc:taf:japsta:v:28:y:2001:i:1:p:129-143
    DOI: 10.1080/02664760120011653
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    References listed on IDEAS

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    1. D. Collett, 1980. "Outliers in Circular Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(1), pages 50-57, March.
    2. SenGupta, Ashis, 1991. "A review of optimality of multivariate tests," Statistics & Probability Letters, Elsevier, vol. 12(6), pages 527-535, December.
    3. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
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    Cited by:

    1. Pewsey, Arthur, 2008. "The wrapped stable family of distributions as a flexible model for circular data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1516-1523, January.
    2. S. Liu & T. Ma & A. SenGupta & K. Shimizu & M.-Z. Wang, 2017. "Influence Diagnostics in Possibly Asymmetric Circular-Linear Multivariate Regression Models," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(1), pages 76-93, May.
    3. Gómez, Héctor W. & Quintana, Fernando A. & Torres, Francisco J., 2007. "A new family of slash-distributions with elliptical contours," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 717-725, April.

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