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.     

Optimal designs for exponential regression

This paper is concerned with the optimal design problem for the particular case of non-linear parametrisation:the parameters to be estimated are included in exponents.Some properties of locally optimal designs as functions of estimated parameters are investigated and a table of such designs in given.We consider also designs to be optimal in the sense of minimax approach.     

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.     

On Calculations Involving the Maximum Cell Frequency

We describe a method of computing the cumulative distribution function of the maximum and minimum cell frequencies in sampling distributions commonly encountered in the analysis of categorical data.The procedure is efficient for exact or approximate calculation in both homogeneous and non-homogeneous cases, is non-recursive, and does not require Dirichlet integrals.Some related statistical problems are also discussed.     

参差重复频率分析和设计

雷达工作于脉冲工作状态时不可避免的会出现盲速现象。可通过参差重频的方法减少盲速带来的影响。在推导频率响应的基础上,该文采用最优化设计的方法进行参差周期的设计,详细考虑并推导得到了最优化搜索中几个重要参数,给出了其解析表达式。仿真结果和频率响应图表明,该方法得到的参差周期能将慢速扩大到原来盲速的数倍以上,有效地减少了盲速的影响。     

低频度事件保险产品选择谈判决策模型

本文考虑在低频度事件中保险产品选择问题,用效用理论及模糊数学知识建立了产品选择模型,并给出了算例,找到了使双方均满意的最优产品。     

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．     

Combining Food Frequency and Survey Data to Quantify Long-Term Dietary Exposure: A Methyl Mercury Case Study

Twenty-four-hour recall data from the Continuing Survey of Food Intake by Individuals (CSFII) are frequently used to estimate dietary exposure for risk assessment. Food frequency questionnaires are traditional instruments of epidemiological research; however, their application in dietary exposure and risk assessment has been limited. This article presents a probabilistic method of bridging the National Health and Nutrition Examination Survey (NHANES) food frequency and the CSFII data to estimate longitudinal (usual) intake, using a case study of seafood mercury exposures for two population subgroups (females 16 to 49 years and children 1 to 5 years). Two hundred forty-nine CSFII food codes were mapped into 28 NHANES fish/shellfish categories. FDA and state/local seafood mercury data were used. A uniform distribution with minimum and maximum blood-diet ratios of 0.66 to 1.07 was assumed. A probabilistic assessment was conducted to estimate distributions of individual 30-day average daily fish/shellfish intakes, methyl mercury exposure, and blood levels. The upper percentile estimates of fish and shellfish intakes based on the 30-day daily averages were lower than those based on two- and three-day daily averages. These results support previous findings that distributions of "usual" intakes based on a small number of consumption days provide overestimates in the upper percentiles. About 10% of the females (16 to 49 years) and children (1 to 5 years) may be exposed to mercury levels above the EPA's RfD. The predicted 75th and 90th percentile blood mercury levels for the females in the 16-to-49-year group were similar to those reported by NHANES. The predicted 90th percentile blood mercury levels for children in the 1-to-5-year subgroup was similar to NHANES and the 75th percentile estimates were slightly above the NHANES.