The DOI matches its Crossref record; 21 of the 21 references it cites were found in a registry or an index.
Generalized Partially Linear Single-Index Models
Abstract
The typical generalized linear model for a regression of a response Y on predictors (X, Z) has conditional mean function based on a linear combination of (X, Z). We generalize these models to have a nonparametric component, replacing the linear combination α T 0X + β T 0Z by η0(α T 0X) + β T 0Z, where η0(·) is an unknown function. We call these generalized partially linear single-index models (GPLSIM). The models include the “single-index” models, which have β0 = 0. Using local linear methods, we propose estimates of the unknown parameters (α0, β0) and the unknown function η0(·) and obtain their asymptotic distributions. Examples illustrate the models and the proposed estimation methodology.
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Cites
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Cited by
An Adaptive Estimation of Dimension Reduction Space
Xia, Y., Tong, H., Li, W. K., & Zhu, L.-X. (2002) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/1467-9868.03411 · Cited by 820
Statistical estimation in varying coefficient models
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Self-citationPenalized Spline Estimation for Partially Linear Single-Index Models
Yu, Y., & Ruppert, D. (2002) · Journal of the American Statistical Association · doi:10.1198/016214502388618861 · Cited by 522
Fan, J., & Li, R. (2004) · Journal of the American Statistical Association · doi:10.1198/016214504000001060 · Cited by 437
Self-citationKai, B., Li, R., & Zou, H. (2011) · The Annals of Statistics · doi:10.1214/10-aos842 · Cited by 301
Metadata
- Authors
- Carroll, R. J., Fan, J., Gijbels, I., & Wand, M. P.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1997-06
- Volume
- 92
- Issue
- 438
- Pages
- 477-489
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2086067392
- Cited by
- 831
- References
- 21
- FWCI
- 11.54
- Type
- journal article
- Language
- en
- Open access
- closed
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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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