Abstract
The regression model $\\mathbf{y} = g(\\mathbf{x}) + \\mathbf{\\varepsilon}$ and least-squares estimation are studied in a general context. By making use of empirical process theory, it is shown that entropy conditions on the class $\\mathscr{G}$ of possible regression functions imply $L^2$-consistency of the least-squares estimator $\\hat{\\mathbf{g}}_n$ of $g$. This result is applied in parametric and nonparametric regression.
Keywords
MathematicsStatisticsEstimatorNonparametric regressionLeast-squares function approximationStrong consistencyGeneralized least squaresContext (archaeology)Regression analysisTotal least squaresConsistency (knowledge bases)Ordinary least squaresApplied mathematicsEconometricsCombinatoricsDiscrete mathematics
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Publication Info
- Year
- 1987
- Type
- article
- Volume
- 15
- Issue
- 2
- Citations
- 45
- Access
- Closed
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Cite This
Sara van de Geer
(1987).
A New Approach to Least-Squares Estimation, with Applications.
The Annals of Statistics
, 15
(2)
.
https://doi.org/10.1214/aos/1176350362
Identifiers
- DOI
- 10.1214/aos/1176350362