摘要
Let(Y,X)be a random vector with its value in R^1×R^d,d(?)1.Let(?)be the collection of real valued functions θ(x) on R^d which is p times differ-entiable at x=0 and p-1 times differentiable on an open neighborhood U ofthe origin of R^d.The conditional distribution of Y is assumed to be of the formof f(y|x,θ(x))dy where θ(x)∈(?)is called the parameter of the family.(Y,X)iscalled a nonparametric median model if furthermore the conditional median of Ygiven X=x is θ(x).In this paper,the optimal rate of convergence for estimatorsof T(θ)=θ(0)is discussed.Under certain conditions,it is proved that for thenonparametric median model the optimal rate of convergence is r=p/(2p+d).A sequence of estimators,which is asymptotically normal with the optimal rate ofcovergence,is constructed.
Let(Y,X)be a random vector with its value in R^1×R^d,d(?)1.Let(?)be the collection of real valued functions θ(x) on R^d which is p times differ-entiable at x=0 and p-1 times differentiable on an open neighborhood U ofthe origin of R^d.The conditional distribution of Y is assumed to be of the formof f(y|x,θ(x))dy where θ(x)∈(?)is called the parameter of the family.(Y,X)iscalled a nonparametric median model if furthermore the conditional median of Ygiven X=x is θ(x).In this paper,the optimal rate of convergence for estimatorsof T(θ)=θ(0)is discussed.Under certain conditions,it is proved that for thenonparametric median model the optimal rate of convergence is r=p/(2p+d).A sequence of estimators,which is asymptotically normal with the optimal rate ofcovergence,is constructed.
基金
This paper was partialy supported by NSFS and Doctoral Programm Foundation of Institution of Higher Education
