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A New Approach to Least-Squares Estimation, with Applications

Sara Van De Geer
The Annals of Statistics
Vol. 15, No. 2 (Jun., 1987), pp. 587-602
Stable URL: http://www.jstor.org/stable/2241327
Page Count: 16
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A New Approach to Least-Squares Estimation, with Applications
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Abstract

The regression model y = g(x) + ε 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 G of possible regression functions imply L2-consistency of the least-squares estimator $\hat{\mathbf{g}}_n$ of g. This result is applied in parametric and nonparametric regression.

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