Using adaptive weighted least squares to reduce the lengths of confidence intervals

The author proposes an adaptive method which produces confidence intervals that are often narrower than those obtained by the traditional procedures. The proposed methods use both a weighted least squares approach to reduce the length of the confidence interval and a permutation technique to insure that its coverage probability is near the nominal level. The author reports simulations comparing the adaptive intervals to the traditional ones for the difference between two population means, for the slope in a simple linear regression, and for the slope in a multiple linear regression having two correlated exogenous variables. He is led to recommend adaptive intervals for sample sizes superior to 40 when the error distribution is not known to be Gaussian.     

Dimensionality reduction approach to multivariate prediction

The authors consider dimensionality reduction methods used for prediction, such as reduced rank regression, principal component regression and partial least squares. They show how it is possible to obtain intermediate solutions by estimating simultaneously the latent variables for the predictors and for the responses. They obtain a continuum of solutions that goes from reduced rank regression to principal component regression via maximum likelihood and least squares estimation. Different solutions are compared using simulated and real data.     

Feature significance in generalized additive models

This paper develops inference for the significance of features such as peaks and valleys observed in additive modeling through an extension of the SiZer-type methodology of Chaudhuri and Marron (1999) and Godtliebsen et al. (2002, 2004) to the case where the outcome is discrete. We consider the problem of determining the significance of features such as peaks or valleys in observed covariate effects both for the case of additive modeling where the main predictor of interest is univariate as well as the problem of studying the significance of features such as peaks, inclines, ridges and valleys when the main predictor of interest is geographical location. We work with low rank radial spline smoothers to allow to the handling of sparse designs and large sample sizes. Reducing the problem to a Generalised Linear Mixed Model (GLMM) framework enables derivation of simulation-based critical value approximations and guards against the problem of multiple inferences over a range of predictor values. Such a reduction also allows for easy adjustment for confounders including those which have an unknown or complex effect on the outcome. A simulation study indicates that our method has satisfactory power. Finally, we illustrate our methodology on several data sets.     

PATTERN RECOGNITION VIA ROBUST SMOOTHING WITH APPLICATION TO LASER DATA

Nowadays airborne laser scanning is used in many territorial studies, providing point data which may contain strong discontinuities. Motivated by the need to interpolate such data and preserve their edges, this paper considers robust nonparametric smoothers. These estimators, when implemented with bounded loss functions, have suitable jump‐preserving properties. Iterative algorithms are developed here, and are equivalent to nonlinear M‐smoothers, but have the advantage of resembling the linear Kernel regression. The selection of their coefficients is carried out by combining cross‐validation and robust‐tuning techniques. Two real case studies and a simulation experiment confirm the validity of the method; in particular, the performance in building recognition is excellent.     

Adaptive sampling without replacement of clusters

In a common form of adaptive cluster sampling, an initial sample of units is selected by random sampling without replacement and, whenever the observed value of the unit is sufficiently high, its neighboring units are added to the sample, with the process of adding neighbors repeated if any of the added units are also high valued. In this way, an initial selection of a high-valued unit results in the addition of the entire network of surrounding high-valued units and some low-valued “edge” units where sampling stops. Repeat selections can occur when more than one initially selected unit is in the same network or when an edge unit is shared by more than one added network. Adaptive sampling without replacement of networks avoids some of this repeat selection by sequentially selecting initial sample units only from the part of the population not already in any selected network. The design proposed in this paper carries this step further by selecting initial units only from the population, exclusive of any previously selected networks or edge units.     

企业经济活动预测问题的一种数学模型及其应用

介绍了企业经济活动预测问题的一种数学模型 ,通过矩阵的运算 ,运用Matlab数学软件 ,使问题迅速得到解决 ,并通过举例说明了其应用     

不可压缩管流的广义有限元方法

本文将广义有限元法用于求解不可压缩管流.通过泛函的变域变分理论推导出严格的网格自适应性条件,可以在给定网格节点数目的条件下,在计算时自动调整网格的分布,使泛函取得极值,同时也使流场参数和网格节点位置取得最优值.对一维喷管的计算结果表明,广义有限元法理论上严密,在计算中是可行的,是常规有限元法向高精度的自适应网格方向的合理推广.     

用神经网络预测碳钢表面合金化处理后的耐腐蚀性能

采用ＢＰ神经网络建立了碳钢表面合金化处理后的耐腐蚀性能的预测模型,分析了网络结构对预测精度的影响,神经网络将寻求序列规律的过程转化为Ｒ＾ｎ→Ｒ＾ｍ逼近的非线性映射的非线性优化问题,适当增加输入单元的历史序列样本,可以得到对序列更为精确的预测,存在最优隐含层节点数。最后进行实际预测,结果表明,这一预测方法对金属材料耐腐蚀试验有指导意义,并具有一定的实用价值。     

基于Haar小波变换的无失真图像压缩

提出了一种利用Ｈａａｒ小波进行图像无失真压缩的算法。对线性预测后的图像进行Ｈａａｒ小波分解,将各子带小波系数根据大小分解成两部分,其位置信息分别通过自适应算术编码进行了有效的压缩。试验结果表明,该算法实现简单,达到了很好的压缩效果。     

非线性混沌经济时序的预测方法及其应用研究

主要研究由非线性混沌经济时序所确定的动力系统的预测方法及其应用 ,通过改进的最优化方法来估计模型的参数 ,并在其相空间中对时序的未来值进行预测 .给出有代表性的实例对模型和算法进行验证 ,结果发现选取最佳的模型阶数能增加预测的准确程度 ,且混沌时序不可能进行长期的预测