MIMCA: multiple imputation for categorical variables with multiple correspondence analysis

We propose a multiple imputation method to deal with incomplete categorical data. This method imputes the missing entries using the principal component method dedicated to categorical data: multiple correspondence analysis (MCA). The uncertainty concerning the parameters of the imputation model is reflected using a non-parametric bootstrap. Multiple imputation using MCA (MIMCA) requires estimating a small number of parameters due to the dimensionality reduction property of MCA. It allows the user to impute a large range of data sets. In particular, a high number of categories per variable, a high number of variables or a small number of individuals are not an issue for MIMCA. Through a simulation study based on real data sets, the method is assessed and compared to the reference methods (multiple imputation using the loglinear model, multiple imputation by logistic regressions) as well to the latest works on the topic (multiple imputation by random forests or by the Dirichlet process mixture of products of multinomial distributions model). The proposed method provides a good point estimate of the parameters of the analysis model considered, such as the coefficients of a main effects logistic regression model, and a reliable estimate of the variability of the estimators. In addition, MIMCA has the great advantage that it is substantially less time consuming on data sets of high dimensions than the other multiple imputation methods.     

The impact of child support on child health

The broad goals of child support policy are to keep children in single-parent families out of poverty and to make sure that their material needs are met. One potentially important, but relatively understudied, set of measures of child well-being are health outcomes. A fixed-effects analysis of data from the Child and Young Adult file of the 1979 National Longitudinal Survey of Youth shows that, conditional upon receipt of some amount of child support, higher payment levels are associated with significantly greater odds of having private health insurance coverage and significantly lower odds of poor or declining health status. These effects persist even after controlling for other factors that are likely to be correlated with child support payments, including total family income and paternal visitation patterns.     

Local composite quantile regression estimation of time-varying parameter vector for multidimensional time-inhomogeneous diffusion models

This paper is dedicated to the study of the composite quantile regression (CQR) estimations of time-varying parameter vectors for multidimensional diffusion models. Based on the local linear fitting for parameter vectors, we propose the local linear CQR estimations of the drift parameter vectors, and verify their asymptotic biases, asymptotic variances and asymptotic normality. Moreover, we discuss the asymptotic relative efficiency (ARE) of the local linear CQR estimations with respect to the local linear least-squares estimations. We obtain that the local estimations that we proposed are much more efficient than the local linear least-squares estimations. Simulation studies are constructed to show the performance of the estimations proposed.     

中国明代白银货币政策与商品竞争力分析

16世纪中叶,由于新航路的开辟,世界市场形成,白银成为世界货币。中国由于是白银贫矿国,在明代之前一直实施铜铸币和纸币政策,只是在明代中叶之后对白银货币实施了放任的政策。由于中国人多地少,劳动力十分廉价,这样以白银为计价单位所表示的商品价格极为低廉。欧洲由于人均土地资源高于中国,人均薪资也高于中国,而且白银供应极为充沛,在一般日用品价格上,远远高于中国。因而,在一般商品价格竞争上,总体不敌中国。当时美洲和日本盛产白银,是世界白银的价格洼地,欧洲又实施了较为自由的贸易政策。这样控制白银的欧洲、日本和掌握世界最低廉商品的中国,相互之间都有极为旺盛的需求,于是,世界市场很快就形成了美洲、日本白银与中国商品交换的格局。     

当前我国社会组织培育和发展中的问题与对策

努力培育和发展社会组织,尽快形成党委领导、政府负责、社会协同、公众参与的公共服务和公共管理新格局,以便提供更多更好的公共服务和公共物品,使人民群众能够在更高水平上实现安居乐业,是我们面临的新历史使命.归纳当前我国社会组织培育和发展工作中形成的新认识,揭示我国社会组织培育和发展中现存的主要问题并探讨解决问题的对策,可为我国社会组织培育和发展工作的有效展开提供借鉴.     

众语喧哗时代的平民化“交响乐”——解读电影《辛亥革命》

为纪念辛亥革命100周年而拍摄的电影《辛亥革命》,—改传统主旋律电影的套路,意识形态日趋淡化,叙事视角以小见大,审美权重多元均衡。这表明,我国主旋律电影其宏观意识形态和历史观点一直呈现出进步的态势。     

The empirical Bayes estimators of the parameter of the Poisson distribution with a conjugate gamma prior under Stein's loss function

For the hierarchical Poisson and gamma model, we calculate the Bayes posterior estimator of the parameter of the Poisson distribution under Stein's loss function which penalizes gross overestimation and gross underestimation equally and the corresponding Posterior Expected Stein's Loss (PESL). We also obtain the Bayes posterior estimator of the parameter under the squared error loss and the corresponding PESL. Moreover, we obtain the empirical Bayes estimators of the parameter of the Poisson distribution with a conjugate gamma prior by two methods. In numerical simulations, we have illustrated: The two inequalities of the Bayes posterior estimators and the PESLs; the moment estimators and the Maximum Likelihood Estimators (MLEs) are consistent estimators of the hyperparameters; the goodness-of-fit of the model to the simulated data. The numerical results indicate that the MLEs are better than the moment estimators when estimating the hyperparameters. Finally, we exploit the attendance data on 314 high school juniors from two urban high schools to illustrate our theoretical studies.     

An Extended Single‐index Model with Missing Response at Random

An extended single‐index model is considered when responses are missing at random. A three‐step estimation procedure is developed to define an estimator for the single‐index parameter vector by a joint estimating equation. The proposed estimator is shown to be asymptotically normal. An algorithm for computing this estimator is proposed. This algorithm only involves one‐dimensional nonparametric smoothers, thereby avoiding the data sparsity problem caused by high model dimensionality. Some simulation studies are conducted to investigate the finite sample performances of the proposed estimators.     

Quadratic Approximation via the SCAD Penalty with a Diverging Number of Parameters

The high-dimensional data arises in diverse fields of sciences, engineering and humanities. Variable selection plays an important role in dealing with high dimensional statistical modelling. In this article, we study the variable selection of quadratic approximation via the smoothly clipped absolute deviation (SCAD) penalty with a diverging number of parameters. We provide a unified method to select variables and estimate parameters for various of high dimensional models. Under appropriate conditions and with a proper regularization parameter, we show that the estimator has consistency and sparsity, and the estimators of nonzero coefficients enjoy the asymptotic normality as they would have if the zero coefficients were known in advance. In addition, under some mild conditions, we can obtain the global solution of the penalized objective function with the SCAD penalty. Numerical studies and a real data analysis are carried out to confirm the performance of the proposed method.