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Studying the bandwidth in $$k$$ -sample smooth tests

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  • Pablo Martínez-Camblor
  • Jacobo Uña-Álvarez

Abstract

In this paper, the problem of bandwidth choice in smooth k-sample tests is considered. Three different bootstrap methods are discussed and implemented. All the methods persecute the bandwidth leading to the maximum power, while preserving the level of the test. The relative performance of the methods is investigated in a simulation study. Illustration through real medical data is provided. The main conclusion is that the bootstrap minimum method provides a good compromise between statistical power and conservativeness. Robustness of the methods with respect to the number of bootstrap resamples and practical limitations are discussed. Copyright Springer-Verlag 2013

Suggested Citation

  • Pablo Martínez-Camblor & Jacobo Uña-Álvarez, 2013. "Studying the bandwidth in $$k$$ -sample smooth tests," Computational Statistics, Springer, vol. 28(2), pages 875-892, April.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:2:p:875-892
    DOI: 10.1007/s00180-012-0333-1
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    References listed on IDEAS

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    1. Ricardo Cao & Gábor Lugosi, 2005. "Goodness‐of‐fit Tests Based on the Kernel Density Estimator," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(4), pages 599-616, December.
    2. Duc Devroye & J. Beirlant & R. Cao & R. Fraiman & P. Hall & M. Jones & Gábor Lugosi & E. Mammen & J. Marron & C. Sánchez-Sellero & J. Uña & F. Udina & L. Devroye, 1997. "Universal smoothing factor selection in density estimation: theory and practice," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(2), pages 223-320, December.
    3. Gao, Jiti & Gijbels, Irène, 2008. "Bandwidth Selection in Nonparametric Kernel Testing," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1584-1594.
    4. Djamal Louani, 1998. "Large Deviations Limit Theorems for the Kernel Density Estimator," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 243-253, March.
    5. Zhang, Jin & Wu, Yuehua, 2007. "k-Sample tests based on the likelihood ratio," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4682-4691, May.
    6. Anderson, N. H. & Hall, P. & Titterington, D. M., 1994. "Two-Sample Test Statistics for Measuring Discrepancies Between Two Multivariate Probability Density Functions Using Kernel-Based Density Estimates," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 41-54, July.
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