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Studying the bandwidth in \(k\)-sample smooth tests

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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.

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Acknowledgments

The authors are grateful to Nerea Larrañaga (Subdirección de Salud Pública de Gipuzkoa) and her colleagues for permission to use the breast cancer data. This work was supported by the Grant MTM2011-23204 of the Spanish Ministry of Science and Innovation (FEDER support included. Second author was also supported by the research Grant MTM2008-03129 of the Spanish Ministerio de Ciencia e Innovación, and by the Grant 10PXIB300068PR of the Xunta de Galicia.

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Authors and Affiliations

  1. Oficina de Investigación Biosanitaria, Asturies, Spain

    Pablo Martínez-Camblor

  2. Departamento de Estadística e IO, Universidad de Vigo, Vigo, Spain

    Jacobo de Uña-Álvarez

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  1. Pablo Martínez-Camblor
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  2. Jacobo de Uña-Álvarez
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Correspondence to Pablo Martínez-Camblor.

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Martínez-Camblor, P., de Uña-Álvarez, J. Studying the bandwidth in \(k\)-sample smooth tests. Comput Stat 28, 875–892 (2013). https://doi.org/10.1007/s00180-012-0333-1

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