Kernel Smoothing in Partial Linear Models
Abstract
SUMMARY: Kernel smoothing is studied in partial linear models, i.e. semiparametric models of the form yi=ξi′β+f(ti)+εi(1⩽i⩽n), where the ξi are fixed known p vectors, β is an unknown vector parameter and f is a smooth but unknown function. Two methods of estimating β and f are considered, one related to partial smoothing splines and the other motivated by partial residual analysis. Under suitable assumptions, the asymptotic bias and variance are obtained for both methods, and it is shown that estimating β by partial residuals results in improved bias with no asymptotic loss in variance. Application to analysis of covariance is made, and several examples are presented.
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The discrepancy in the results for 3 df/year between the NS and PS approaches has a theoretical basis related to the tradeoff between the parametric and nonparametric components of the PS models in explaining variation in the outcome variable.
“The discrepancy in the results for 3 df/year between the NS and PS approaches has a theoretical basis related to the tradeoff between the parametric and nonparametric components of the PS models in explaining variation in the outcome variable (Peng et al. 2006; Speckman 1988).”
From Acute effects of ambient ozone on mortality in Europe and North America: results from the APHENA study (2013) · cites this paper as Speckman 1988
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- Authors
- Speckman, P.
- Affiliations
- University of Missouri (US)
- Corresponding author
- Speckman, Paul
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 1988-07-01
- Volume
- 50
- Issue
- 3
- Pages
- 413-436
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W135795571
- Cited by
- 986
- References
- 41
- Citations by year
- 2026: 11 · 2025: 27 · 2024: 18 · 2023: 21 · 2022: 28 · 2021: 25 · 2020: 38 · 2019: 35 · 2018: 33 · 2017: 38 · 2016: 32 · 2015: 39 · 2014: 33 · 2013: 48 · 2012: 40
- FWCI
- 4.39
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
- Locations
- Journal of the Royal Statistical Society Series B (Statistical Methodology) (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Keywords
- kernel smoothing, partially linear models, semiparametric regression, asymptotic bias, asymptotic variance, covariance analysis, nonparametric estimation
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