Under some mild conditions, we establish a strong Bahadur representation of a general class of nonparametric local linear M-estimators for mixing processes on a random field. If the socalled optimal bandwidth hn = O（...Under some mild conditions, we establish a strong Bahadur representation of a general class of nonparametric local linear M-estimators for mixing processes on a random field. If the socalled optimal bandwidth hn = O（｜n｜^-1/5）, n ∈ Z^d, is chosen, then the remainder rates in the Bahadur representation for the local M-estimators of the regression function and its derivative are of order O（｜n｜^-4/5 log ｜n｜）. Moreover, we derive some asymptotic properties for the nonparametric local linear M-estimators as applications of our result.展开更多
In this article the authors establish the Bahadur type representations for the kernel quantileestimator and the kernel estimator of the derivatives of the quantile function on the basis of lefttruncated and right cens...In this article the authors establish the Bahadur type representations for the kernel quantileestimator and the kernel estimator of the derivatives of the quantile function on the basis of lefttruncated and right censored data. Under suitable conditions, with probability one, the exactconvergence rate of the remainder term in the representations is obtained. As a by-product, theLIL, the asymptotic normality for those kernel estimators are derived.展开更多
A kernel-type estimator of the quantile function Q（p） = inf{t：F（t） ≥ p}, 0 ≤ p ≤ 1, is proposed based on the kernel smoother when the data are subjected to random truncation. The Bahadur-type representations o...A kernel-type estimator of the quantile function Q（p） = inf{t：F（t） ≥ p}, 0 ≤ p ≤ 1, is proposed based on the kernel smoother when the data are subjected to random truncation. The Bahadur-type representations of the kernel smooth estimator are established, and from Bahadur representations the authors can show that this estimator is strongly consistent, asymptotically normal, and weakly convergent.展开更多
In this paper, we consider a change point model allowing at most one change, X($\tfrac{i}{n}$\tfrac{i}{n}) = f($\tfrac{i}{n}$\tfrac{i}{n}) + e($\tfrac{i}{n}$\tfrac{i}{n}), where f(t) = α + θ $I_{(t_0 ,1)} $I_{(t_0 ,...In this paper, we consider a change point model allowing at most one change, X($\tfrac{i}{n}$\tfrac{i}{n}) = f($\tfrac{i}{n}$\tfrac{i}{n}) + e($\tfrac{i}{n}$\tfrac{i}{n}), where f(t) = α + θ $I_{(t_0 ,1)} $I_{(t_0 ,1)} (t), 0 ≤ t ≤ 1, {e($\tfrac{1}{n}$\tfrac{1}{n}), ..., e($\tfrac{n}{n}$\tfrac{n}{n})} is a sequence of i.i.d. random variables distributed as e with 0 being the median of e. For this change point model, hypothesis test problem about the change-point t0 is studied and a test statistic is constructed. Furthermore, a nonparametric estimator of t0 is proposed and shown to be strongly consistent. Finally, we give an estimator of jump θ and obtain it’s asymptotic property. Performance of the proposed approach is investigated by extensive simulation studies.展开更多
基金National Natural Science Foundation of China (No.10771192)
文摘Under some mild conditions, we establish a strong Bahadur representation of a general class of nonparametric local linear M-estimators for mixing processes on a random field. If the socalled optimal bandwidth hn = O（｜n｜^-1/5）, n ∈ Z^d, is chosen, then the remainder rates in the Bahadur representation for the local M-estimators of the regression function and its derivative are of order O（｜n｜^-4/5 log ｜n｜）. Moreover, we derive some asymptotic properties for the nonparametric local linear M-estimators as applications of our result.
文摘In this article the authors establish the Bahadur type representations for the kernel quantileestimator and the kernel estimator of the derivatives of the quantile function on the basis of lefttruncated and right censored data. Under suitable conditions, with probability one, the exactconvergence rate of the remainder term in the representations is obtained. As a by-product, theLIL, the asymptotic normality for those kernel estimators are derived.
基金Zhou's research was partially supported by the NNSF of China (10471140, 10571169)Wu's research was partially supported by NNSF of China (0571170)
文摘A kernel-type estimator of the quantile function Q（p） = inf{t：F（t） ≥ p}, 0 ≤ p ≤ 1, is proposed based on the kernel smoother when the data are subjected to random truncation. The Bahadur-type representations of the kernel smooth estimator are established, and from Bahadur representations the authors can show that this estimator is strongly consistent, asymptotically normal, and weakly convergent.
基金National Natural Science Foundation of China (Grant No.10471136)Ph.D.Program Foundation of the Ministry of Education of ChinaSpecial Foundations of the Chinese Academy of Sciences and USTC
文摘In this paper, we consider a change point model allowing at most one change, X($\tfrac{i}{n}$\tfrac{i}{n}) = f($\tfrac{i}{n}$\tfrac{i}{n}) + e($\tfrac{i}{n}$\tfrac{i}{n}), where f(t) = α + θ $I_{(t_0 ,1)} $I_{(t_0 ,1)} (t), 0 ≤ t ≤ 1, {e($\tfrac{1}{n}$\tfrac{1}{n}), ..., e($\tfrac{n}{n}$\tfrac{n}{n})} is a sequence of i.i.d. random variables distributed as e with 0 being the median of e. For this change point model, hypothesis test problem about the change-point t0 is studied and a test statistic is constructed. Furthermore, a nonparametric estimator of t0 is proposed and shown to be strongly consistent. Finally, we give an estimator of jump θ and obtain it’s asymptotic property. Performance of the proposed approach is investigated by extensive simulation studies.
