# Modified nonparametric kernel estimates of a regression function and their consistencies with rates

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## Summary

Two sets of modified kernel estimates of a regression function are proposed: one when a bound on the regression function is known and the other when nothing of this sort is at hand. Explicit bounds on the mean square errors of the estimators are obtained. Pointwise as well as uniform consistency in mean square and consistency in probability of the estimators are proved. Speed of convergence in each case is investigated.

## Key words and phrases

Regression curve retraction mean square weak pointwise uniform consistency rates## Preview

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© The Institute of Statistical Mathematics, Tokyo 1987