A note on the universal consistency of the kernel distribution function estimator |
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| Authors: | José E Chacón Alberto Rodríguez-Casal |
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| Institution: | 1. Departamento de Matemáticas, Universidad de Extremadura, Badajoz, Spain;2. Departamento de Estatística e Investigación Operativa, Universidade de Santiago de Compostela, Santiago de Compostela, Spain |
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| Abstract: | The problem of universal consistency of data driven bandwidth selectors for the kernel distribution estimator is analyzed. We provide a uniform in bandwidth result for the kernel estimate of a continuous distribution function. Our smoothness assumption is minimal in the sense that if the true distribution function has some discontinuity then the kernel estimate is no longer consistent. |
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