Rates of convergence for nearest neighbor estimators with the smoother regression function

Details Rates of convergence for nearest neighbor estimators with the smoother regression function Rates of convergence for nearest neighbor estimators with the smoother regression function

2011-02-28

arxiv.org/abs/1102.5633v1

Mathematics

Statistics Theory

12 pages, 1 table

Scientific paper

In regression analysis one wants to estimate the regression function from a data. In this paper we consider the rate of convergence for the nearest neighbor estimator in case that the regression function is $(p,C)$-smooth. It is an open problem whether the optimal rate can be achieved by some nearest neighbor estimator in case that $p$ is on (1,1.5]. We solve the problem affirmatively. This is the main result of this paper. Throughout this paper, we assume that the data is independent and identically distributed and as an error criterion we use the expected $L_2$ error.

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