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On Optimal Global Rates Of Convergence For Nonparametric Regression With Random Design
, 2000
"... this paper is to show that it is possible to achieve for ksmooth regression functions the wellknown optimal global rate of convergence n ..."
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this paper is to show that it is possible to achieve for ksmooth regression functions the wellknown optimal global rate of convergence n
Strong Consistency of Automatic Kernel Regression Estimates
, 2001
"... Regression function estimation from independent and identically distributed bounded data is considered. The L 2 error with integration with respect to the design measure is used as an error criterion. It is shown that the kernel regression estimate with an arbitrary random bandwidth is weakly and st ..."
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Regression function estimation from independent and identically distributed bounded data is considered. The L 2 error with integration with respect to the design measure is used as an error criterion. It is shown that the kernel regression estimate with an arbitrary random bandwidth is weakly and strongly consistent for all distributions whenever the random bandwidth is chosen from some deterministic interval whose upper and lower bounds satisfy the usual conditions used to prove consistency of the kernel estimate for deterministic bandwidths. Choosing discrete bandwidths by crossvalidation allows to weaken the conditions on the bandwidths. Key words and phrases: automatic kernel estimates, crossvalidation, regression estimates, strong consistency. 1