The DOI matches its Crossref record; 16 of the 16 references it cites were found in a registry or an index.
Local Linear Regression Smoothers and Their Minimax Efficiencies
Open accessAbstract
In this paper we introduce a smooth version of local linear regression estimators and address their advantages. The MSE and MISE of the estimators are computed explicitly. It turns out that the local linear regression smoothers have nice sampling properties and high minimax efficiency-they are not only efficient in rates but also nearly efficient in constant factors. In the nonparametric regression context, the asymptotic minimax lower bound is developed via the heuristic of the "hardest onedimensional subproblem" of Donoho and Liu. Connections of the minimax risk with the modulus of continuity are made. The lower bound is also applicable for estimating conditional mean (regression) and conditional quantiles for both fixed and random design regression problems.
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Cites
Robust Locally Weighted Regression and Smoothing Scatterplots
Cleveland, W. S. (1979) · Journal of the American Statistical Association · doi:10.1080/01621459.1979.10481038 · Cited by 11,594
Nadaraya, E. A. (1964) · Theory of Probability & Its Applications · doi:10.1137/1109020 · Cited by 3,462
Consistent Nonparametric Regression
Stone, C. J. (1977) · The Annals of Statistics · doi:10.1214/aos/1176343886 · Cited by 1,792
Asymptotic Methods in Statistical Decision Theory
Cam, L. L. (1986) · Springer Series in Statistics · doi:10.1007/978-1-4612-4946-7 · Cited by 1,317
Design-adaptive Nonparametric Regression
Fan, J. (1992) · Journal of the American Statistical Association · doi:10.1080/01621459.1992.10476255 · Cited by 1,268
Self-citationOptimal Rates of Convergence for Nonparametric Estimators
Stone, C. J. (1980) · The Annals of Statistics · doi:10.1214/aos/1176345206 · Cited by 795
Statistical Estimation and Optimal Recovery
Donoho, D. L. (1994) · The Annals of Statistics · doi:10.1214/aos/1176325367 · Cited by 263
Weighted Local Regression and Kernel Methods for Nonparametric Curve Fitting
Müller, H. (1987) · Journal of the American Statistical Association · doi:10.1080/01621459.1987.10478425 · Cited by 188
Linear Estimation for Approximately Linear Models
Sacks, J., & Ylvisaker, D. (1978) · The Annals of Statistics · doi:10.1214/aos/1176344315 · Cited by 153
Minimax Estimation of the Mean of a Normal Distribution when the Parameter Space is Restricted
Bickel, P. J. (1981) · The Annals of Statistics · doi:10.1214/aos/1176345646 · Cited by 143
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Matching As An Econometric Evaluation Estimator
Heckman, J. J., Ichimura, H., & Todd, P. (1998) · Review of Economic Studies · doi:10.1111/1467-937x.00044 · Cited by 3,807
Does matching overcome lalonde’s critique of nonexperimental estimators?
A. Smith, J., & E. Todd, P. (2005) · Journal of Econometrics · doi:10.1016/j.jeconom.2004.04.011 · Cited by 3,176
Tripney, J., Hombrados, J., Newman, M., Hovish, K., Brown, C., Steinka-Fry, K., & Wilkey, E. (2013) · Campbell Systematic Reviews: Better Evidence for a Better World · doi:10.4073/csr.2013.9 · Cited by 72
Metadata
- Authors
- Fan, J.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1993-03-01
- Volume
- 21
- Issue
- 1
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2027244596
- Cited by
- 894
- References
- 16
- FWCI
- 27.78
- Type
- journal article
- Language
- en
- Open access
- bronze
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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