Robust confidence regions for multinomial probabilities

Generally, confidence regions for the probabilities of a multinomial population are constructed based on the Pearson χ² statistic. Morales et al. (Bootstrap confidence regions in multinomial sampling. Appl Math Comput. 2004;155:295–315) considered the bootstrap and asymptotic confidence regions based on a broader family of test statistics known as power-divergence test statistics. In this study, we extend their work and propose penalized power-divergence test statistics-based confidence regions. We only consider small sample sizes where asymptotic properties fail and alternative methods are needed. Both bootstrap and asymptotic confidence regions are constructed. We consider the percentile and the bias corrected and accelerated bootstrap confidence regions. The latter confidence region has not been studied previously for the power-divergence statistics much less for the penalized ones. Designed simulation studies are carried out to calculate average coverage probabilities. Mean absolute deviation between actual and nominal coverage probabilities is used to compare the proposed confidence regions.     

法律职业主义视野下的香港律师惩戒制度

香港的律师制度渊源于英国,在律师团体管理方面表现出自主性、自律性的特点,具有典型的法律职业主义色彩。香港的律师惩戒制度作为体现上述特点的主要内容之一,具有民主性、程序性、公正性和司法性特征。具有法律职业主义色彩的律师伦理规范和律师惩戒制度,体现了社会一部分职业相对于国家所具有的独立性,但同时也是律师团体通过自我控制实现市场垄断所作出的努力。香港律师团体管理模式中所具有的这种两面性为大陆律师管理模式的改革和完善提供了很难得的研究样本。     

Alternative Penalty Functions for Penalized Likelihood Principal Components

The penalized likelihood principal component method of Park (2005) offers flexibility in the choice of the penalty function. This flexibility allows the method to be tailored to enhance interpretation in special cases. Of particular interest is a penalty function in the style of the Lasso that can be used to produce exactly zero loadings. Also of interest is a penalty function for cases in which interpretability is best represented by alignment with orthogonal subspaces, rather than with axis directions. In each case, a data example is presented.     

面板数据的自适应Lasso分位回归方法研究

如何在对参数进行估计的同时自动选择重要解释变量,一直是面板数据分位回归模型中讨论的热点问题之一。通过构造一种含多重随机效应的贝叶斯分层分位回归模型,在假定固定效应系数先验服从一种新的条件Laplace分布的基础上,给出了模型参数估计的Gibbs抽样算法。考虑到不同重要程度的解释变量权重系数压缩程度应该不同,所构造的先验信息具有自适应性的特点,能够准确地对模型中重要解释变量进行自动选取,且设计的切片Gibbs抽样算法能够快速有效地解决模型中各个参数的后验均值估计问题。模拟结果显示,新方法在参数估计精确度和变量选择准确度上均优于现有文献的常用方法。通过对中国各地区多个宏观经济指标的面板数据进行建模分析,演示了新方法估计参数与挑选变量的能力。     

BAYESIAN HYPER‐LASSOS WITH NON‐CONVEX PENALIZATION

The Lasso has sparked interest in the use of penalization of the log‐likelihood for variable selection, as well as for shrinkage. We are particularly interested in the more‐variables‐than‐observations case of characteristic importance for modern data. The Bayesian interpretation of the Lasso as the maximum a posteriori estimate of the regression coefficients, which have been given independent, double exponential prior distributions, is adopted. Generalizing this prior provides a family of hyper‐Lasso penalty functions, which includes the quasi‐Cauchy distribution of Johnstone and Silverman as a special case. The properties of this approach, including the oracle property, are explored, and an EM algorithm for inference in regression problems is described. The posterior is multi‐modal, and we suggest a strategy of using a set of perfectly fitting random starting values to explore modes in different regions of the parameter space. Simulations show that our procedure provides significant improvements on a range of established procedures, and we provide an example from chemometrics.     

The Partial Linear Model in High Dimensions

Partial linear models have been widely used as flexible method for modelling linear components in conjunction with non‐parametric ones. Despite the presence of the non‐parametric part, the linear, parametric part can under certain conditions be estimated with parametric rate. In this paper, we consider a high‐dimensional linear part. We show that it can be estimated with oracle rates, using the least absolute shrinkage and selection operator penalty for the linear part and a smoothness penalty for the nonparametric part.     

A Note on Application of Nesterov’s Method in Solving Lasso-Type Problems

Many different algorithms have been proposed to solve penalized variable selection problems, in particular lasso and its variants, including group lasso and fused lasso. Loss functions other than quadratic loss also pose significant challenges for finding efficient solvers. Here, we note that Nesterov’s method can be used to transform an optimization problem with general smooth convex loss to quadratic loss with identity covariate matrix in each iteration. After such reduction, the problem becomes much easier to solve or even can be solved in closed form in some cases. We perform some simulations and apply our implementation to phoneme discrimination.     

Adjusted power-divergence test statistics for simple goodness-of-fit under clustered sampling

Two-different types of adjustments to the power-divergence test statistics have been introduced for the problem of testing goodness-of-fit under clustered sampling. Penalization has also been introduced to handle the cells with zero frequencies. The asymptotic distribution of the proposed power-divergence test statistics has been investigated under clustered sampling and the performances of the proposed statistics for finite samples have been studied through a designed simulation study.     

Regularized Bayesian quantile regression

A number of nonstationary models have been developed to estimate extreme events as function of covariates. A quantile regression (QR) model is a statistical approach intended to estimate and conduct inference about the conditional quantile functions. In this article, we focus on the simultaneous variable selection and parameter estimation through penalized quantile regression. We conducted a comparison of regularized Quantile Regression model with B-Splines in Bayesian framework. Regularization is based on penalty and aims to favor parsimonious model, especially in the case of large dimension space. The prior distributions related to the penalties are detailed. Five penalties (Lasso, Ridge, SCAD0, SCAD1 and SCAD2) are considered with their equivalent expressions in Bayesian framework. The regularized quantile estimates are then compared to the maximum likelihood estimates with respect to the sample size. A Markov Chain Monte Carlo (MCMC) algorithms are developed for each hierarchical model to simulate the conditional posterior distribution of the quantiles. Results indicate that the SCAD0 and Lasso have the best performance for quantile estimation according to Relative Mean Biais (RMB) and the Relative Mean-Error (RME) criteria, especially in the case of heavy distributed errors. A case study of the annual maximum precipitation at Charlo, Eastern Canada, with the Pacific North Atlantic climate index as covariate is presented.     

劳动力市场匹配效率的影响因素研究

当前就业难、用工荒并存的重要原因是劳动力市场不健全导致匹配效率低。本文基于面板数据,利用自适应Lasso方法对我国劳动力市场匹配效率的影响因素进行实证研究。研究发现,技工学校等职业培训机构、人才市场等职业市场机构的发展对劳动力市场匹配效率有显著影响,相对于需求方而言,提高匹配效率应更多从供给侧入手,这是根本之策。应整合优化职业教育资源,提高劳动力质量和适用性,更好地满足加快建设创新型国家、全面建设现代化经济体系的需要。