In this paper,we present a detailed description of the limiting behaviorof local oscillation of the uniform empirical process.As an application,we estab-lish the laws of the iterated logarithm for the“naive”estimato...In this paper,we present a detailed description of the limiting behaviorof local oscillation of the uniform empirical process.As an application,we estab-lish the laws of the iterated logarithm for the“naive”estimator and the nearestneighbor estimator of the density function.When compared to those of Hall andHong,the conditions of the bandwidth imposed here are as weak as possible.展开更多
Let（X,Y） be a pair of R<sup>d</sup>×R<sup>1</sup>-valued random variables.In thispaper we investigate the asymptotic properties of the L<sub>1</sub>-norm kernel estimator oft...Let（X,Y） be a pair of R<sup>d</sup>×R<sup>1</sup>-valued random variables.In thispaper we investigate the asymptotic properties of the L<sub>1</sub>-norm kernel estimator ofthe conditional median function of Y on X.Under appropriate regularity condi-tions,asymptotic normality and the optimal rates of convergence n<sup>（-1）/（2+d）</sup>and(n<sup>-1</sup>log n)<sup>1/（2+d）</sup> in the L<sup>q</sup>（1（?）q【∞）-and L<sup>∞</sup>-norms restricted to a compactset,respectively,are obtained.Our study shows that this estimator and the well-known Nadaraya-Watson’s kernel estimator of the conditional mean function of Yon X have the same asymptotic properties.展开更多
基金Research supported by National Natural Science Foundation of China
文摘In this paper,we present a detailed description of the limiting behaviorof local oscillation of the uniform empirical process.As an application,we estab-lish the laws of the iterated logarithm for the“naive”estimator and the nearestneighbor estimator of the density function.When compared to those of Hall andHong,the conditions of the bandwidth imposed here are as weak as possible.
基金Research supported by National Natural Science Foundation of China
文摘Let（X,Y） be a pair of R<sup>d</sup>×R<sup>1</sup>-valued random variables.In thispaper we investigate the asymptotic properties of the L<sub>1</sub>-norm kernel estimator ofthe conditional median function of Y on X.Under appropriate regularity condi-tions,asymptotic normality and the optimal rates of convergence n<sup>（-1）/（2+d）</sup>and(n<sup>-1</sup>log n)<sup>1/（2+d）</sup> in the L<sup>q</sup>（1（?）q【∞）-and L<sup>∞</sup>-norms restricted to a compactset,respectively,are obtained.Our study shows that this estimator and the well-known Nadaraya-Watson’s kernel estimator of the conditional mean function of Yon X have the same asymptotic properties.
