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Kernels for Nonparametric Curve Estimation
Abstract
SUMMARY: The choice of kernels for the nonparametric estimation of regression functions and of their derivatives is investigated. Explicit expressions are obtained for kernels minimizing the asymptotic variance or the asymptotic integrated mean square error, IMSE (the present proof of the optimality of the latter kernels is restricted up to order k = 5). These kernels are also of interest for the nonparametric estimation of probability densities and spectral densities. A finite sample study indicates that higher order kernels – asymptotically improving the rate of convergence – may become attractive for realistic finite sample size. Suitably modified kernels are considered for estimating at the extremities of the data, in a way which allows to retain the order of the bias found for interior points.
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Citations
Cites
Formulas and Theorems for the Special Functions of Mathematical Physics
Magnus, W., Oberhettinger, F., & Soni, R. P. (1966) · doi:10.1007/978-3-662-11761-3 · Cited by 3,469
Cited by
Kernel Smoothing in Partial Linear Models
Speckman, P. (1988) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1988.tb01738.x · Cited by 986
Chapter 38 Applied nonparametric methods
Härdle, W., & Linton, O. (1994) · Handbook of Econometrics · doi:10.1016/s1573-4412(05)80007-8 · Cited by 325
Alignment of curves by dynamic time warping
Wang, K., & Gasser, T. (1997) · The Annals of Statistics · doi:10.1214/aos/1069362747 · Cited by 293
Self-citationRubin, D. B. (2010) · American Journal of Ophthalmology · doi:10.1016/j.ajo.2009.08.024 · Cited by 88
Sleep and circadian rhythm during a short space mission
Gundel, A., Nalishiti, V., Reucher, E., Vejvoda, M., & Zulley, J. (1993) · The Clinical Investigator · doi:10.1007/bf00209726 · Cited by 65
Metadata
- Authors
- Gasser, T., MÜller, H.-G., & Mammitzsch, V.
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 1985-01-01
- Volume
- 47
- Issue
- 2
- Pages
- 238-252
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W157032409
- Cited by
- 470
- References
- 1
- FWCI
- 10.98
- Type
- journal article
- Language
- en
- Open access
- closed
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- Gasser, T., MÜller, H.-G., & Mammitzsch, V. (1985). Kernels for Nonparametric Curve Estimation. Journal of the Royal Statistical Society Series B: Statistical Methodology. https://doi.org/10.1111/j.2517-6161.1985.tb01350.x
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