Abstract
The monotone rearrrangement algorithm was introduced by Hardy, Littlewood and Po ́lya as a sorting device for functions. As- suming that x is a monotone function and that an estimate xn of x is given, consider the monotone rearrangement xˆn of xn. This new estimator is shown to be uniformly consistent. Under suitable as- sumptions, pointwise limit distribution results for xˆn 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.
| Original language | English |
|---|---|
| Pages (from-to) | 549-583 |
| Number of pages | 43 |
| Journal | Bernoulli |
| Volume | 25 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2019 |
Subject classification (UKÄ)
- Probability Theory and Statistics
Free keywords
- Limit distributions
- regression function es- timation
- monotone rearrangement.
- dependence
- density estimation