A New Approach to Least-Squares Estimation, with Applications
Geer, Sara Van De
Ann. Statist., Tome 15 (1987) no. 1, p. 587-602 / Harvested from Project Euclid
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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.
Publié le : 1987-06-14
Classification:  Consistency,  entropy,  empirical measure,  uniform convergence,  60B10,  60G50,  62J05 
@article{1176350362,
     author = {Geer, Sara Van De},
     title = {A New Approach to Least-Squares Estimation, with Applications},
     journal = {Ann. Statist.},
     volume = {15},
     number = {1},
     year = {1987},
     pages = { 587-602},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176350362}
}

Geer, Sara Van De. A New Approach to Least-Squares Estimation, with Applications. Ann. Statist., Tome 15 (1987) no. 1, pp.  587-602. http://gdmltest.u-ga.fr/item/1176350362/