General m-esttmators and applications to bounded influence estimation for non-linear regression

In this paper, we study the M-estimators in the case that λ_F:(β)=E_F:(φ(Z,β))=0 has more than one solution, We show that the numerical iterative procedures converge and that the resulting estimators are consistent and asymptotically normal. We apply them to the non-linear regression models, and then, we find an optimal M-estimate among those that have bounded gross error sensitivity.     

Asymptotic robustness of least median of squares for autoregressions with additive outliers

This paper considers the robustness properties in the time series context of the least median of squares (LMS) estimator. The influence function of the LMS estimator is derived under additive outlier contamination. This influence function is redescending and bounded for fixed values of the AR parameters. The gross-error sensitivity, however, is an unbounded function of the AR parameters. In order to asses the global robustness behavior of the LMS estimator, we consider several notions of breakdown. The breakdown points of the LMS estimator depend on the value of the underlying AR parameter. Generally, the breakdown point is below one half for high values of the AR parameter. The bias curves of the LMS estimator reveal, however, that the magnitude of outliers has to be considerable in order to cause breakdown.     

Further influence measures in factor analysis

Various influence measures are discussed for sensitivity analysis in factor analysis. The internal norm is used to characterize the vector-valued influence curves in factor analysis. Influence curves for the chi-square goodness of fit test, and the determinants of the model covariance matrix and unique variance matrix are derived. They are found to have simple formulas which are easy to be interpreted and have nice distributions for calibration. The likelihood displacement is also applied to sensitivity analysis in maximum likelihood factor analysis.     

ROC Curves in Non‐Parametric Location‐Scale Regression Models

Abstract. The receiver operating characteristic (ROC) curve is a tool of extensive use to analyse the discrimination capability of a diagnostic variable in medical studies. In certain situations, the presence of a covariate related to the diagnostic variable can increase the discriminating power of the ROC curve. In this article, we model the effect of the covariate over the diagnostic variable by means of non‐parametric location‐scale regression models. We propose a new non‐parametric estimator of the conditional ROC curve and study its asymptotic properties. We also present some simulations and an illustration to a data set concerning diagnosis of diabetes.     

地理教育的现状与改革的思考

高考文科取消地理科目后，中学地理教育及高师地理教育均受到冲击，但地理科学的特殊地位决定了它是不可能被取代的．地理科学的发展应在应用方面找出路，并不断深化地理教育改革．     

The ℓ1 oblique procrustes problem

In this paper, we reconsider the well-known oblique Procrustes problem where the usual least-squares objective function is replaced by a more robust discrepancy measure, based on the ₁ norm or smooth approximations of it.We propose two approaches to the solution of this problem. One approach is based on convex analysis and uses the structure of the problem to permit a solution to the ₁ norm problem. An alternative approach is to smooth the problem by working with smooth approximations to the ₁ norm, and this leads to a solution process based on the solution of ordinary differential equations on manifolds. The general weighted Procrustes problem (both orthogonal and oblique) can also be solved by the latter approach. Numerical examples to illustrate the algorithms which have been developed are reported and analyzed.     

Book Reviews

This article examines some difficulties associated with the Haynes–Stone model and attempts to clarify how the model can be justified as representing the hypothesis that “quantity is demand determined and price is supply determined.” It also argues that the applications of such a model as was done by Haynes and Stone might not have resolved the controversies related to the Phillips curve and the supply function of exports (or imports).     

论代理契约中决策方案的设计与选择

本文论述了以博奕关系简化复杂的代理关系,用必然等值评估代理人的优先选择曲线,根据代理人优先选择曲线的类型,分析代理人的风险态度,据以设计相应的激励方案的方法与过程.     

基于环境学习曲线的山东省SO2排放及节能减排潜力分析

基于1981—2006年的数据对山东省SO2排放的规律进行研究，得到山东省SO2排放的环境学习曲线。应用这一曲线，定量分析山东省17个地级市减少SO2排放的潜力，并结合2006年各市的万元GDP能耗情况，对它们的节能减排潜力进行综合评价。     

儿童拼图性识字的记忆研究

以艾宾浩斯的遗忘曲线为基本框架,通过拼图性学习和常规性学习两种不同学习生字方法的实验比较,对儿童识字的一般性规律进行研究。得到结论:拼图性识字在记忆的保持上优于常规性识字;拼图性识字在学习有笔画难度的字上优于常规性识字;拼图性识字同样符合艾宾浩斯的遗忘曲线规律。拼图性识字教学符合儿童以动作思维为主的认识特点,符合儿童心理的年龄特征,能提高对字形记忆的效果,让儿童可以有效、有趣、自主进行早期识字学习。