Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift
By Lawrence D. Brown, Andrew V. Carter, Mark G. Low, Cun-Hui Zhang. 2004
73 citations recorded by the source corpus.
This paper establishes the global asymptotic equivalence between a Poisson process with variable intensity and white noise with drift under sharp smoothness conditions on the unknown function. This equivalence is also extended to density estimation models by Poissonization. The asymptotic equivalences are established by constructing explicit equivalence mappings. The impact of such asymptotic equivalence results is that an investigation in one of these nonparametric models automatically yields asymptotically analogous results in the other models.
Subfields: Finance, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/993fd33f5dd7c797d44e7095e67c27a4fc88d57e
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Finance
- A. van der Vaart
- Harrison H. Zhou
- James M. Robins
- Judith Rousseau
- Markus Reiß
- Subhashis Ghosal
- Richard Nickl
- I. Castillo
In Statistics and Probability
- A. van der Vaart
- James M. Robins
- Harrison H. Zhou
- Victor Chernozhukov
- Edward H. Kennedy
- Tommaso Cai
- Michael R. Kosorok
- Stefan Wager
Citations in the corpus
- Asymptotic equivalence of spectral density estimation and gaussian white noise (2009, background): “[6] succeeded in weakening the Hölder ball condition in [26] to a condition that is compact both in the Besov spaces B 2,2 and B 1/2 4,4 on the unit interval.”
- Adaptive nonparametric confidence sets (2006, background): “(The latter objection is alleviated by the recent constructions of Brown, Carter, Low and Zhang [10].”