相依误差广义线性模型的M估计的Bahadur表示

考虑如下广义线性模型y_i=h(x~T_i,β)+e_i=1,2,…,n,其中e_i=G(…,ε_(i-1),ε_i),h是一个连续可导函数,ε_i是独立同分布的随机变量,并且它的期望为0,方差σ~2有限.本文给出了参数β的M估计,并且得到了该估计的Bahadur表示,该结论推广了线性模型的相关结论.应用M估计的Bahadur表示,得到了相依误差的线性回归模型,poisson模型,logistic模型和独立误差的广义线性模型等模型的渐近性质.     

Robustness for Inhomogeneous Poisson Point Processes

We consider robustness for estimation of parametric inhomogeneous Poisson point processes. We propose an influence functional to measure the effect of contamination on estimates. We also propose an M-estimator as an alternative to maximum likelihood estimator, show its consistency and asymptotic normality.     

基于鲁棒M估计和Mean Shift聚类的动态背景下运动目标检测

针对动态背景下运动目标的检测问题,提出了一种基于鲁棒M估计和Mean Shift聚类的目标检测新方法。首先,在考虑全局光照变化的情况下,构建鲁棒M估计器估计全局运动,以实现最小化相邻2帧图像中所有像素亮度的绝对残差和,根据M估计得到像素点权值,提取出代表局部运动信息的离群点;在离群点中均匀抽取网格点,然后利用Mean Shift聚类算法实现不同运动点的分割;根据聚类的结果生成凸包,准确分割出运动目标区域。实验结果表明,该方法能检测出动态背景下的多个运动目标区域,多目标检测准确度到达95%以上,并且只需两帧图像就可以准确检测并锁定运动目标,满足实时处理的要求,具有一定的工程意义.     

随机适应误差下线性模型参数M估计的渐近性质

在一些较弱的充分条件下,本文研究了误差为随机适应序列下,线性模型回归参数M估计的强相合性.与文献中已有结果比较,扩大了应用范围,且对矩条件也有较大改进.同时我们给出了随机适应误差下线性模型参数M估计的渐近正态性.     

左截断相依数据下非参数回归的局部M 估计

本文对左截断模型, 利用局部多项式的方法构造了非参数回归函数的局部M 估计. 在观察样本为平稳α-混合序列下, 建立了该估计量的强弱相合性以及渐近正态性. 模拟研究显示回归函数的局部M 估计比Nadaraya-Watson 型估计和局部多项式估计更稳健.     

Variable bandwidth and one-step local M-estimator

A robust version of local linear regression smoothers augmented with variable bandwidth is studied. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming of lack of robustness of least-squares techniques. The use of variable bandwidth enhances the flexibility of the resulting local M-estimators and makes them possible to cope well with spatially inhomogeneous curves, heteroscedastic errors and nonuniform design densities. Under appropriate regularity conditions, it is shown that the proposed estimators exist and are asymptotically normal. Based on the robust estimation equation, one-step local M-estimators are introduced to reduce computational burden. It is demonstrated that the one-step local M-estimators share the same asymptotic distributions as the fully iterative M-estimators, as long as the initial estimators are good enough. In other words, the one-step local M-estimators reduce significantly the computation cost of the fully iterative M-estimators without deteriorating their performance. This fact is also illustrated via simulations.     

Empirical Likelihood Type Confidence Intervals Under Random Censorship

In this paper a simple way to obtain empirical likelihood type confidenceintervals for the mean under random censorship is suggested. An extension tothe more general case where the functional of interest is an M-functional isdiscussed and the proposed technique is used to construct confidenceintervals for quantiles. The results of a simulation study carried out toassess the accuracy of these inferential procedures are also given.     

Large Deviation and Other Results for Minimum Contrast Estimators

A number of authors have been concerned with constructing large deviation approximations to densities and probabilities associated with minimum contrast estimators (equivalently, M-estimators) using a tilting approach due to Field. These developments are an interesting and important extension of saddlepoint-type methodology. However, in the case of a multivariate parameter, the theoretical picture has remained incomplete in certain respects, as explained below. In this paper we present results which provide rigorous justification of the tilting argument, using conditions which it is feasible to check. These results include a new formulation and proof of Skovgaard's theorem for the intensity of minimum contrast estimators, but under conditions which are typically straightforward to check in practice. Our most detailed application is to multivariate location-scatter models.     

Linear Huber M-Estimator Under Ellipsoidal Data Uncertainty

The purpose of this note is to present a robust counterpart of the Huber estimation problem in the sense of Ben-Tal and Nemirovski when the data elements are subject to ellipsoidal uncertainty. The robust counterparts are polynomially solvable second-order cone programs with the strong duality property. We illustrate the effectiveness of the robust counterpart approach on a numerical example.     

Adaptive penalized M-estimation with current status data

Current status data arises when a continuous response is reduced to an indicator of whether the response is greater or less than a random threshold value. In this article we consider adaptive penalized M-estimators (including the penalized least squares estimators and the penalized maximum likelihood estimators) for nonparametric and semiparametric models with current status data, under the assumption that the unknown nonparametric parameters belong to unknown Sobolev spaces. The Cox model is used as a representative of the semiparametric models. It is shown that the modified penalized M-estimators of the nonparametric parameters can achieve adaptive convergence rates, even when the degrees of smoothing are not known in advance. consistency, asymptotic normality and inference based on the weighted bootstrap for the estimators of the regression parameter in the Cox model are also established. A simulation study is conducted for the Cox model to evaluate the finite sample efficacy of the proposed approach and to compare it with the ordinary maximum likelihood estimator. It is demonstrated that the proposed method is computationally superior.We apply the proposed approach to the California Partner Study analysis.