Least Trimmed Squares Estimator in the Errors-in-Variables Model

We propose a robust estimator in the errors-in-variables model using the least trimmed squares estimator. We call this estimator the orthogonal least trimmed squares (OLTS) estimator. We show that the OLTS estimator has the high breakdown point and appropriate equivariance properties. We develop an algorithm for the OLTS estimate. Simulations are performed to compare the efficiencies of the OLTS estimates with the total least squares (TLS) estimates and a numerical example is given to illustrate the effectiveness of the estimate.     

On the explosion rate of maximum-bias functions

The maxbias function B_T() contains much information about the robustness properties of the estimate T. This function satisfies B_T(0)=0 and B_T()<for all 0<<whereis the breakdown point of T. Hampel (1974)pioneered the study of the limiting behaviour of B_T(?) where ? → 0. He computed and optimized the rate γ at which B_T(?) approaches 0 when ? → 0. This rate is now called the contamination sensitivity of T, and constitutes one of the cornerstones of the theory of robustness. We show that much can also be learned from the study of the limiting behaviour of B_T(?) when ? → ?*. A new robustness measure, called the relative explosion rate, can be obtained by studying the limiting relative maxbias behaviour of two extimates when approaches their common breakdown point ?*. Like the contamination sensitivity, the relative explosion rate can be readily derived from the estimate's score function. General formulae are given for M-estimates of scale and S-, MM- and τ-estimates of regression. We also show that the maxbias behaviour for large ? is largely determined by the curvature of the estimate's score function near zero. This motivates our definition and study of the local order of a score function.     

Finite sample tail behaviour of hodges-lehmann type estimators

The tail behavior of Hodges-Lehmann type location estimators is studied with respect to a tail performance measure. The result obtained here generalizes and complements the corresponding work on R-estimators of JurecKova (1981a). The connection between the tail behavior and the breakdown point discovered in He, Jureckova Koenker and Portnoy (1990) for regression and monotone location estimators is extended to Hodges-Lehmann type location estimators, confirming the important role of the tail behavior as a measure of robustness of estimators.     

Robust Estimation of Multivariate Linear Model Based on Depth Weighted Mean and Scatter

Based on the projection depth weighted mean and scatter estimation of the joint distribution of (x, y), we introduce a robust estimator of the regression coefficients for the multivariate linear model. The new estimator possesses desirable properties including affine invariance, Fisher consistency, and asymptotic normality. Also, we study the robustness of the estimator in terms of breakdown point and influence function. Extensive simulation studies are performed to investigate the finite sample behavior of robustness and efficiency. The methodology is illustrated with a real data example.     

Robust Multivariate Outlier Labeling

A criterion for robust estimation of location and covariance matrix is considered, and its application in outlier labeling is discussed. This method, unlike the methods based on MVE and MCD, is applicable to large and high-dimension data sets. The method proposed here is also robust and has the same breakdown point as the MVE- and MCD-based methods. Furthermore, the computational complexity of the proposed method is significantly smaller than that of other methods.     

青年“躺平”现象的析与破

青年“躺平”现象是在现代社会的快节奏生活、现代信息技术的快速发展、多元不良思潮的冲击裹挟之中滋生与蔓延的。在“躺平”现象影响下，青年的理想信念根基被侵蚀、自我价值认同被弱化、奋斗精神被消解。必须从优化社会大环境、加强互联网正向引领、增强青年自我价值认同入手，积极引导青年一代成为新时代的奋进者、开拓者、担当者，以永不懈怠的精神状态、永不停滞的前进姿态，驱散“躺平”的消极影响，唱响青春主旋律，不断增强青年的志气、骨气和底气，在接续奋斗中将中华民族伟大复兴的中国梦变为现实。