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arXiv · 0710.4617

Limit properties of the monotone rearrangement for density and regression function estimation

Dragi Anevski·Anne-Laure Fougères
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Abstract

The monotone rearrrangement algorithm was introduced by Hardy, Littlewood and Pólya as a sorting device for functions. Assuming that $x$ is a monotone function and that an estimate $x_n$ of $x$ is given, consider the monotone rearrangement $\hat{x}_n$ of $x_n$. This new estimator is shown to be uniformly consistent. Under suitable assumptions, pointwise limit distribution results for $\hat{x}_n$ are obtained. The framework is general and allows for weakly dependent and long range dependent stationary data. Applications in monotone density and regression function estimation are detailed.

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Dragi Anevski, Anne-Laure Fougères. 2007-10-25. Limit properties of the monotone rearrangement for density and regression function estimation. https://arxiv.org/abs/0710.4617

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