Summary
Let (X, Y) be a ℝdxℝ-valued random vector and let r(t)=E(Y/X=t) be the regression function of Y on X that has to be estimated from a sample (X i, Yi), i=1,..., n. We establish conditions ensuring that an estimate of the form
Where Φni(t, x) is a sequence of Borel measurable functions on ℝdxℝd, is uniformly strongly consistent with a certain rate of convergence. Applying this result we obtain rates of strong uniform consistency of the regressogram, kernel estimates, k n-nearest neighbor estimates and estimates based on orthogonal series.
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Liero, H. Strong uniform consistency of nonparametric regression function estimates. Probab. Th. Rel. Fields 82, 587–614 (1989). https://doi.org/10.1007/BF00341285
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DOI: https://doi.org/10.1007/BF00341285