Sensitivity analysis of M-estimates

Bahadur representation of the difference of estimators of regression coefficients for the full data set and for the set from which one observation was deleted is given for the M-estimators which are generated by a continuous -function. The representation is invariant with respect to the scale of residuals and it indicates that the bound of the norm of the difference is proportional to the gross error sensitivity. Then for the -function which corresponds to the median it is shown that the difference of the estimates for the full data and for data without one observation, although being bounded in probability, can be much larger than indicated by the gross error sensitivity.     

A Finite-Difference Scheme for a Nonlinear Model of Wood Drying Process

In this paper, we discuss the construction and analysis of a finite-difference scheme for solving a system of two nonlinear differential equations. The mathematical model describes the process of moisture motion in a wood. The wood is treated as a porous medium. The stability analysis of the finite-difference scheme is done in the maximum norm. Stability and a priori error estimates are proved.     

基于非线性回归分析的棉纤维水分快速测量模型

为了克服现有棉纤维水分测量方法中 ,烘箱法存在耗能费时、直流电阻法存在测试结果稳定性较差等缺陷 ,提出基于交流阻抗法的棉纤维水分快速测试新方法 .实验发现 ,其测试结果 (电测值 )与棉纤维实际回潮率呈非线性相关 .通过多元非线性回归分析 ,建立了棉纤维电测值与回潮率值的多元非线性回归模型 .经稳定性分析与误差分析 ,证实了该回归模型能够较好地拟合棉纤维回潮率值 .回归模型的建立 ,为基于交流阻抗法的智能型棉纤维水分快速测试仪设计打下了基础     

Sensitivity of risk measures with respect to the normal approximation of total claim distributions

A simple and commonly used method to approximate the total claim distribution of a (possibly weakly dependent) insurance collective is the normal approximation. In this article, we investigate the error made when the normal approximation is plugged in a fairly general distribution-invariant risk measure. We focus on the rate of convergence of the error relative to the number of clients, we specify the relative error’s asymptotic distribution, and we illustrate our results by means of a numerical example. Regarding the risk measure, we take into account distortion risk measures as well as distribution-invariant coherent risk measures.