Abstract
A bootstrap-based choice of bandwidth for kernel density estimation is introduced. The method works by estimating the integrated mean squared error (IMSE) for any given bandwidth and then minimizing over all bandwidths. A straightforward application of the bootstrap method to estimate the IMSE fails because it does not capture the bias component. A smoothed bootstrap method based on an initial density estimate is described that solves this problem. It is possible to construct pointwise and simultaneous confidence intervals for the density. The simulation study compares cross-validation and the bootstrap method over a wide range of densities—a long-tailed, a short-tailed, an asymmetric, and a bimodal, among others. The bootstrap method uniformly outperforms cross-validation. The accuracy of the constructed confidence bands improves as the sample size increases.
Original language | English |
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Pages (from-to) | 1119-1122 |
Number of pages | 4 |
Journal | Journal of the American Statistical Association |
Volume | 85 |
Issue number | 412 |
DOIs | |
Publication status | Published - 1 Jan 1990 |
Funding
• Julian J. Faraway is Assistant Professor, Department of Statistics, University of Michigan, Ann Arbor, MI 48109. Myoungshic Jhun is Associate Professor, Department of Statistics, Korea University, Seoul, 136-701 Korea. This research was supported by the Korea Science and Engineering Foundation. The authors thank an associate editor and two referees for improving the quality of this article.
Keywords
- Confidence bands
- Cross-validation
- Kernel density estimation
- Smoothed bootstrap
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty