A remedy for kernel estimation under random design
(1996) Statistics : a journal of theoretical and applied statistics — Vol. 28, n° 3, p. 201-225 (1996)
Files
No attached file found for this publication.
Details
- Authors
- Abstract
- Two common kernel-based methods for non-parametric repression estimation suffer from well-known drawbacks when the design is random. The Gasser-Muller estimator is inadmissible due to its high variance while the Nadaraya-Watson estimator has zero asymptotic efficiency because of poor bias behavior. Under asymptotic consideration, the local linear estimator avoids these two drawbacks of kernel estimators and achieves minimax optimality. However, when based on compact support kernels its finite sample behavior is disappointing because sudden kinks may show up in the estimate. This paper proposes a modification of the kernel estimator, called the binned convolution estimator leading to a fast O(n) method. Provided the design density is continously differentiable and the conditional fourth moments exist the binned convolution estimator has asymptotic properties identical with those of the local linear estimator.
- Affiliations
Citations
Kneip, A., & Engel, J. (1996). A remedy for kernel estimation under random design. Statistics : a journal of theoretical and applied statistics, 28(3), 201-225. https://doi.org/10.1080/02331889708802561 (Original work published 1996)