Iterated Data Sharpening

Abstract

Data sharpening in kernel regression has been shown to be an effective method of reducing bias while having minimal effects on variance. Earlier efforts to iterate the data sharpening procedure have been less effective, due to the employment of an inappropriate sharpening transformation. In this article, an iterated data sharpening algorithm is proposed which reduces the asymptotic bias at each iteration, while having modest effects on the variance. The efficacy of the iterative approach is demonstrated theoretically and via a simulation study. Boundary effects persist and the affected region successively grows when the iteration is applied to local constant regression. By contrast, boundary bias successively decreases for each iteration step when applied to local linear regression. This study also shows that after iteration, the resulting estimates are less sensitive to bandwidth choice, and a further simulation study demonstrates that iterated data sharpening with data-driven bandwidth selection via cross-validation can lead to more accurate regression function estimation. Examples with real data are used to illustrate the scope of change made possible by using iterated data sharpening and to also identify its limitations. Supplementary materials for this article are available online.

Keywords:

• Bandwidth selection
• Bias reduction
• Cross-validation
• Local polynomial regression

Acknowledgments

We are grateful to Richard Lockhart for helpful comments, and to the Associate Editor and one referee for constructive comments.

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

The first author is grateful for support in the form of a MITACS Globalinks scholarship, the second and third authors are grateful for research support from the Natural Sciences and Engineering Research Council of Canada and from the Canada Foundation for Innovation, the NSERC Alliance International Catalyst Grant ALLRP 590341-23, and the University of British Columbia Okanagan (UBC-O) Vice Principal Research Office in collaboration with the UBC-O Irving K. Barber Faculty of Science.