Outlier detection and robust variable selection via the penalized weighted LAD-LASSO method

This paper studies the outlier detection and robust variable selection problem in the linear regression model. The penalized weighted least absolute deviation (PWLAD) regression estimation method and the adaptive least absolute shrinkage and selection operator (LASSO) are combined to simultaneously achieve outlier detection, and robust variable selection. An iterative algorithm is proposed to solve the proposed optimization problem. Monte Carlo studies are evaluated the finite-sample performance of the proposed methods. The results indicate that the finite sample performance of the proposed methods performs better than that of the existing methods when there are leverage points or outliers in the response variable or explanatory variables. Finally, we apply the proposed methodology to analyze two real datasets.     

"昙花一现"的美丽——朦胧诗回眸

朦胧诗是新时期文学的第一个诗歌潮流,它是一代人生命体验的艺术折光,凸现了自我意识,带来了诗歌审美的嬗变和精神重建的要求。朦胧诗的诗人们呼喊人道主义和要求人的尊严、价值等的启蒙主题,以及大胆借鉴西方现代派的艺术手法的探索精神,无疑是一座崛起的丰碑,已经深深烙在人们心里。然而,朦胧诗由于不可避免的局限性和精神危机,在更为激进的新生代诗人的一片打倒声中,走向消亡。     

南京国民政府公务员考选制度的近代化意义

南京国民政府公务员考选制度是中国历史上第一个准现代化的人事考试制度,考选人才方面既吸收了古代考试的公平精神又采纳了西方文官考试的先进理念,具备了近代化的特征。从人才的选拔看具备了公平性,但体制的缺陷使其任用的成效不尽人意,阻碍了它近代化的进程。     

重塑学生自信心的情感教学法初探

现代教育培养的人才应具有健全的人格、较强的创新精神和实践能力,善于协作和敢于竞争.然而,目前高校中有相当一部分学生因为学习成绩差等原因而丧失自信心,陷入不良情感的心理障碍中不能自拔.基于人本主义学习理论的情感教学法注重教学过程中的师生互动和情感交流,能够有效地促使学生重塑自信心,恢复积极向上的健康心态.情感教学法可从五个环节来实施:(1)简介课程的概况,确立课程的学习目标,对学生进行积极的鼓励;(2)调查学生的情况,将学生进行合理分组;(3)在教学过程中将课程知识传授、能力培养与信心培养相结合;(4)实行阶段考察,鼓励学生进一步学习;(5)课程结束时对"差生"实施积极的补救措施.     

Subsampling-extrapolation bandwidth selection in bivariate kernel density estimation

This paper focuses on bivariate kernel density estimation that bridges the gap between univariate and multivariate applications. We propose a subsampling-extrapolation bandwidth matrix selector that improves the reliability of the conventional cross-validation method. The proposed procedure combines a U-statistic expression of the mean integrated squared error and asymptotic theory, and can be used in both cases of diagonal bandwidth matrix and unconstrained bandwidth matrix. In the subsampling stage, one takes advantage of the reduced variability of estimating the bandwidth matrix at a smaller subsample size m (m < n); in the extrapolation stage, a simple linear extrapolation is used to remove the incurred bias. Simulation studies reveal that the proposed method reduces the variability of the cross-validation method by about 50% and achieves an expected integrated squared error that is up to 30% smaller than that of the benchmark cross-validation. It shows comparable or improved performance compared to other competitors across six distributions in terms of the expected integrated squared error. We prove that the components of the selected bivariate bandwidth matrix have an asymptotic multivariate normal distribution, and also present the relative rate of convergence of the proposed bandwidth selector.     

Model selection in high-dimensional noisy data: a simulation study

In many practical applications, high-dimensional regression analyses have to take into account measurement error in the covariates. It is thus necessary to extend regularization methods, that can handle the situation where the number of covariates p largely exceed the sample size n, to the case in which covariates are also mismeasured. A variety of methods are available in this context, but many of them rely on knowledge about the measurement error and the structure of its covariance matrix. In this paper, we set the goal to compare some of these methods, focusing on situations relevant for practical applications. In particular, we will evaluate these methods in setups in which the measurement error distribution and dependence structure are not known and have to be estimated from data. Our focus is on variable selection, and the evaluation is based on extensive simulations.     

Learning from a lot: Empirical Bayes for high‐dimensional model‐based prediction

Empirical Bayes is a versatile approach to “learn from a lot” in two ways: first, from a large number of variables and, second, from a potentially large amount of prior information, for example, stored in public repositories. We review applications of a variety of empirical Bayes methods to several well‐known model‐based prediction methods, including penalized regression, linear discriminant analysis, and Bayesian models with sparse or dense priors. We discuss “formal” empirical Bayes methods that maximize the marginal likelihood but also more informal approaches based on other data summaries. We contrast empirical Bayes to cross‐validation and full Bayes and discuss hybrid approaches. To study the relation between the quality of an empirical Bayes estimator and p, the number of variables, we consider a simple empirical Bayes estimator in a linear model setting. We argue that empirical Bayes is particularly useful when the prior contains multiple parameters, which model a priori information on variables termed “co‐data”. In particular, we present two novel examples that allow for co‐data: first, a Bayesian spike‐and‐slab setting that facilitates inclusion of multiple co‐data sources and types and, second, a hybrid empirical Bayes–full Bayes ridge regression approach for estimation of the posterior predictive interval.     

Hard thresholding regression

In this paper, we propose the hard thresholding regression (HTR) for estimating high‐dimensional sparse linear regression models. HTR uses a two‐stage convex algorithm to approximate the ?₀‐penalized regression: The first stage calculates a coarse initial estimator, and the second stage identifies the oracle estimator by borrowing information from the first one. Theoretically, the HTR estimator achieves the strong oracle property over a wide range of regularization parameters. Numerical examples and a real data example lend further support to our proposed methodology.     

Instrumental variable based variable selection for generalized linear models with endogenous covariates

We study the variable selection problem for a class of generalized linear models with endogenous covariates. Based on the instrumental variable adjustment technology and the smooth-threshold estimating equation (SEE) method, we propose an instrumental variable based variable selection procedure. The proposed variable selection method can attenuate the effect of endogeneity in covariates, and is easy for application in practice. Some theoretical results are also derived such as the consistency of the proposed variable selection procedure and the convergence rate of the resulting estimator. Further, some simulation studies and a real data analysis are conducted to evaluate the performance of the proposed method, and simulation results show that the proposed method is workable.