A Nonstationary Statistical Model for Computationally Intensive Numerical Ordinary Differential Systems

ABSTRACT

Computer models depending on unknown inputs are used in computer experiments in order to study the input-output relationship. Some computer models are computationally intensive and only a few computer runs can be made. A nonstationary statistical model that is used as a faster-running surrogate for computationally intensive numerical solvers of ordinary differential systems is proposed in this article. This statistical model reflects the dynamics of the system and, as a population dynamics example will show, it can be more accurate than a commonly used black box statistical model.     

A semiparametric estimator of the distribution function of a variable measured with error

The estimation of the distribution functon of a random variable X measured with error is studied. Let the i-th observation on X be denoted by Y_iX_i+ε_i where ε_i is the measuremen error. Let {Y_i} (i=1,2,…,n) be a sample of independent observations. It is assumed that {X_i} and {∈_i} are mutually independent and each is identically distributed. As is standard in the literature for this problem, the distribution of e is assumed known in the development of the methodology. In practice, the measurement error distribution is estimated from replicate observations.

The proposed semiparametric estimator is derived by estimating the quantises of X on a set of n transformed V-values and smoothing the estimated quantiles using a spline function. The number of parameters of the spline function is determined by the data with a simple criterion, such as AIC. In a simulation study, the semiparametric estimator dominates an optimal kernel estimator and a normal mixture estimator for a wide class of densities.

The proposed estimator is applied to estimate the distribution function of the mean pH value in a field plot. The density function of the measurement error is estimated from repeated measurements of the pH values in a plot, and is treated as known for the estimation of the distribution function of the mean pH value.     

Compare diagnostic tests using transformation-invariant smoothed ROC curves()

Receiver operating characteristic (ROC) curve, plotting true positive rates against false positive rates as threshold varies, is an important tool for evaluating biomarkers in diagnostic medicine studies. By definition, ROC curve is monotone increasing from 0 to 1 and is invariant to any monotone transformation of test results. And it is often a curve with certain level of smoothness when test results from the diseased and non-diseased subjects follow continuous distributions. Most existing ROC curve estimation methods do not guarantee all of these properties. One of the exceptions is Du and Tang (2009) which applies certain monotone spline regression procedure to empirical ROC estimates. However, their method does not consider the inherent correlations between empirical ROC estimates. This makes the derivation of the asymptotic properties very difficult. In this paper we propose a penalized weighted least square estimation method, which incorporates the covariance between empirical ROC estimates as a weight matrix. The resulting estimator satisfies all the aforementioned properties, and we show that it is also consistent. Then a resampling approach is used to extend our method for comparisons of two or more diagnostic tests. Our simulations show a significantly improved performance over the existing method, especially for steep ROC curves. We then apply the proposed method to a cancer diagnostic study that compares several newly developed diagnostic biomarkers to a traditional one.     

做好“绿箱”与“黄箱”文章——谈对中国农业的支持

中国加入WTO意味着政府对农业的支持政策要作重大调整,政策调整的基本取向是打“规则”牌,充分利用WTO的“绿箱”和“黄箱”政策,加大政府对农业的支持力度,从根本上提高中国农业的竞争力。     

“绿箱”措施与农业保护政策的调整

农业的弱势地位及其面临的风险决定了各国需要对其进行适当的保护。"绿箱"措施因其是免于削减的项目而日益成为许多国家农业保护政策的重点。我国已承诺在加入WTO后开放国内农产品市场,过去依赖高关税、复杂的非关税的保护措施将被逐步取消,因此,我国政府对农业的支持应调整为以"绿箱"措施为重点。但是"绿箱"措施的运用在管理体制和支持结构上还存在许多问题。因此,加强和完善"绿箱"措施,将是我国农业保护政策调整的基本方向。     

Generalized additive modelling of sample extremes

Summary.  We describe smooth non-stationary generalized additive modelling for sample extremes, in which spline smoothers are incorporated into models for exceedances over high thresholds. Fitting is by maximum penalized likelihood estimation, with uncertainty assessed by using differences of deviances and bootstrap simulation. The approach is illustrated by using data on extreme winter temperatures in the Swiss Alps, analysis of which shows strong influence of the north Atlantic oscillation. Benefits of the new approach are flexible and appropriate modelling of extremes, more realistic assessment of estimation uncertainty and the accommodation of complex dependence patterns.     

混凝土箱梁顶板横向预应力框架效应分析

针对目前预应力混凝土箱梁腹板开裂现象比较普遍这一现象,拟从预应力混凝土箱梁顶板横向预应力框架效应查找开裂原因。首先,分析了箱梁截面参数对顶板预应力横向框架效应的影响,然后结合具体预应力混凝土连续箱梁桥,分析了预应力混凝土箱梁顶板横向框架效应所引起的腹板竖向拉应力,得到了一些有意义的结论,可为改进该类桥梁的设计提供参考。     

Spline-backfitted kernel smoothing of partially linear additive model

A spline-backfitted kernel smoothing method is proposed for partially linear additive model. Under assumptions of stationarity and geometric mixing, the proposed function and parameter estimators are oracally efficient and fast to compute. Such superior properties are achieved by applying to the data spline smoothing and kernel smoothing consecutively. Simulation experiments with both moderate and large number of variables confirm the asymptotic results. Application to the Boston housing data serves as a practical illustration of the method.     

三态英语教学法重要指标的统计分析--三态英语系统教学理论及其教学法之五

本文通过对教学统计数据的分析和总结,说明三态英语系统教学理论及其教学法的合理性和必要性,以及在当今大学英语教学中所具有的综合性教学运用价值.     

强大的系统分析工具-MATLAB

介绍了MATLAB的组成、特点和它的工具箱.