In this paper, we propose a tilted estimator for nonparametric estimation of a density function. We use a cross-validation criterion to choose both the bandwidth and the tilted estimator parameters. We demonstrate theoretically that our proposed estimator provides a convergence rate which is strictly faster than the usual rate attained using a conventional kernel estimator with a positive kernel. We investigate the performance through both theoretical and numerical studies.
- Cross validation function
- Non-parametric density function estimation
- Rate of convergence
- Tilted estimators