Consistency for the Least Squares Estimator in Non-parametric Regression
نویسندگان
چکیده
We shall study the general regression model Y = g 0 (X) + ", where X and " are independent. The available information about g 0 can be expressed by g 0 2 G for some class G. As an estimator of g 0 we choose the least squares estimator. We shall give necessary and suucient conditions for consistency of this estimator in terms of (basically) geometric properties of G. Our main tool will be the theory of empirical processes.
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