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.     

Fast and approximate exhaustive variable selection for generalised linear models with APES

We present APproximated Exhaustive Search (APES), which enables fast and approximated exhaustive variable selection in Generalised Linear Models (GLMs). While exhaustive variable selection remains as the gold standard in many model selection contexts, traditional exhaustive variable selection suffers from computational feasibility issues. More precisely, there is often a high cost associated with computing maximum likelihood estimates (MLE) for all subsets of GLMs. Efficient algorithms for exhaustive searches exist for linear models, most notably the leaps‐and‐bound algorithm and, more recently, the mixed integer optimisation (MIO) algorithm. The APES method learns from observational weights in a generalised linear regression super‐model and reformulates the GLM problem as a linear regression problem. In this way, APES can approximate a true exhaustive search in the original GLM space. Where exhaustive variable selection is not computationally feasible, we propose a best‐subset search, which also closely approximates a true exhaustive search. APES is made available in both as a standalone R package as well as part of the already existing mplot package.     

行政处罚听证基本原则之解析

行政行为具有单方意志性特征,容易对当事人利益造成损害,因此其实施必须遵循一定的制度要求。而听证作为行政处罚制度的重要内容,对于防止行政机关滥用职权,加强当事人参与程度,保护公民合法权益,提高行政效率起到了积极作用。我国虽然已经建立了听证制度．但从目前来看,还有很多不足,因此必须从完善行证处罚听证基本原则入手,来重构我国行政处罚听证制度。     

地方党政主要领导职位空缺的现状、成因及对策

地方党政主要领导职位空缺是指在领导干部选任和调配过程中,由于诸多常规或非常规原因导致某一地区的党委或政府部门主要领导职位在较长时间内空缺,进而直接或间接影响地方党政工作的特殊现状,广泛存在于各级、各地党政部门。由于我国有关干部职位空缺的制度建设和管理规范尚不完善,地方党政主要领导职位空缺产生一些消极影响,主要表现为不利于地方党政机关运行,存在腐败风险,触发舆论风险等。在充分认识空缺危害性的基础上,深入分析造成职位空缺的干部调配因素、选任导向变革因素以及其他非常规因素等,从完善遴选机制、衔接制度、保障机制、舆论生态治理、干部教育等五个方面切实解决地方党政主要领导职位空缺带来的一系列问题。     

中国古代词选的承传

中国古代词选的承传,主要体现在三条线索中:一是分调选编的承传;二是分类选编的承传;三是分人选编的承传。古代词选的承传,为词作选本发挥欣赏、批评与文献传播的多方面价值产生了积极的作用。