Abstract
Improved kernel-based estimates of integrated squared density derivatives are obtained by reinstating non-stochastic terms that have previously been omitted, and using the bandwidth to (approximately) cancel these positive quantities with the leading smoothing bias terms which are negative. Such estimators have exhibited great practical merit in the context of data-based selection of the bandwidth in kernel density estimation, a motivating application of this work discussed elsewhere.
Original language | English |
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Pages (from-to) | 511-514 |
Number of pages | 4 |
Journal | Statistics and Probability Letters |
Volume | 11 |
Issue number | 6 |
DOIs | |
State | Published - Jun 1991 |
Bibliographical note
Funding Information:further assistance, to Matt Wand for his useful comment and to the referee for forcing certain clarifications. Both the Mathematical Sciences Research Centre of the Australian National University, Canberra, Australia, and the IBM Research Division, Yorktown Heights, New York, USA, supported M.C. Jones during the course of this work.
Keywords
- Bandwidth selection
- bias reduction
- functional estimation
- kernel density estimation
- rates of convergence
- smoothing
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty