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Abstract:
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For univariate i.i.d. samples, two pieces of information are obtained: one is the values of the data, the other is the ranks of the data. Analyses have been carried out on each individually in parametric and non-parametric statistics respectively. However, both can be looked at simultaneously. This work concentrates on how this dual nature of data can be used in kernel based estimation methods. An overview of a density estimator and a regression estimator that use both ranks and data values simultaneously to create a naturally adaptive bandwidth is presented.
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