Asymptotics and optimal bandwidth selection for highest density region estimation
Authors:
- R. J. SamworthRSR. J. Samworth
- M. P. WandM. P. Wand
Open Access
- 1 June 2010
- journal article
- research article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 38 (3) , 1767-1792
Abstract
We study kernel estimation of highest-density regions (HDR). Our main contributions are two-fold. First, we derive a uniform-in-bandwidth asymptotic approximation to a risk that is appropriate for HDR estimation. This approximation is then used to derive a bandwidth selection rule for HDR estimation possessing attractive asymptotic properties. We also present the results of numerical studies that illustrate the benefits of our theory and methodology.Keywords
All Related Versions
This publication has 19 references indexed in Scilit:
- Optimal rates for plug-in estimators of density level setsBernoulli, 2009
- Asymptotic normality of plug-in level set estimatesThe Annals of Applied Probability, 2009
- Total error in a plug-in estimator of level setsStatistics & Probability Letters, 2003
- Convergence rates in nonparametric estimation of level setsStatistics & Probability Letters, 2001
- On nonparametric estimation of density level setsThe Annals of Statistics, 1997
- Measuring Mass Concentrations and Estimating Density Contour Clusters-An Excess Mass ApproachThe Annals of Statistics, 1995
- Exact Mean Integrated Squared ErrorThe Annals of Statistics, 1992
- Comparison of Data-Driven Bandwidth SelectorsJournal of the American Statistical Association, 1990
- Estimation of a Convex Density Contour in Two DimensionsJournal of the American Statistical Association, 1987
- An alternative method of cross-validation for the smoothing of density estimatesBiometrika, 1984