Semiparametric Analysis of Network Formation

ABSTRACT

We consider a statistical model for directed network formation that features both node-specific parameters that capture degree heterogeneity and common parameters that reflect homophily among nodes. The goal is to perform statistical inference on the homophily parameters while treating the node-specific parameters as fixed effects. Jointly estimating all parameters leads to incidental-parameter bias and incorrect inference. As an alternative, we develop an approach based on a sufficient statistic that separates inference on the homophily parameters from estimation of the fixed effects. The estimator is easy to compute and can be applied to both dense and sparse networks, and is shown to have desirable asymptotic properties under sequences of growing networks. We illustrate the improvements of this estimator over maximum likelihood and bias-corrected estimation in a series of numerical experiments. The technique is applied to explain the import and export patterns in a dense network of countries and to estimate a more sparse advice network among attorneys in a corporate law firm.     

A Note on Functional Forms of Order Statistics

Functional forms of order statistics, as the solution of a system of equations, are studied. The case of the smaller and the larger of two random variables is discussed in detail. Some applications for normal and binomial distributions are presented.     

Simulation of the p-generalized Gaussian distribution

In this paper, we introduce the p-generalized polar methods for the simulation of the p-generalized Gaussian distribution. On the basis of geometric measure representations, the well-known Box–Muller method and the Marsaglia–Bray rejecting polar method for the simulation of the Gaussian distribution are generalized to simulate the p-generalized Gaussian distribution, which fits much more flexibly to data than the Gaussian distribution and has already been applied in various fields of modern sciences. To prove the correctness of the p-generalized polar methods, we give stochastic representations, and to demonstrate their adequacy, we perform a comparison of six simulation techniques w.r.t. the goodness of fit and the complexity. The competing methods include adapted general methods and another special method. Furthermore, we prove stochastic representations for all the adapted methods.     

Nonparametric regression with cross‐classified responses

In this article, we develop regression models with cross‐classified responses. Conditional independence structures can be explored/exploited through the selective inclusion/exclusion of terms in a certain functional ANOVA decomposition, and the estimation is done nonparametrically via the penalized likelihood method. A cohort of computational and data analytical tools are presented, which include cross‐validation for smoothing parameter selection, Kullback–Leibler projection for model selection, and Bayesian confidence intervals for odds ratios. Random effects are introduced to model possible correlations such as those found in longitudinal and clustered data. Empirical performances of the methods are explored in simulation studies of limited scales, and a real data example is presented using some eyetracking data from linguistic studies. The techniques are implemented in a suite of R functions, whose usage is briefly described in the appendix. The Canadian Journal of Statistics 39: 591–609; 2011. © 2011 Statistical Society of Canada     

Bootstrap confidence bands for the CDF using ranked-set sampling

In ranked-set sampling (RSS), a stratification by ranks is used to obtain a sample that tends to be more informative than a simple random sample of the same size. Previous work has shown that if the rankings are perfect, then one can use RSS to obtain Kolmogorov–Smirnov type confidence bands for the CDF that are narrower than those obtained under simple random sampling. Here we develop Kolmogorov–Smirnov type confidence bands that work well whether the rankings are perfect or not. These confidence bands are obtained by using a smoothed bootstrap procedure that takes advantage of special features of RSS. We show through a simulation study that the coverage probabilities are close to nominal even for samples with just two or three observations. A new algorithm allows us to avoid the bootstrap simulation step when sample sizes are relatively small.     

Use of prior information for estimating the variance components

The MINQUE and its modifications are considered for estimating the variances of the balanced one-way random effects model. The effects of the a priori values on the estimators of the variances are examined in detail. The Mean Square Errors of the estimators are compared for variations in the prior values of the unknown variances.     

先锋:一种姿态的两种向度

艺术领域内曾被广泛使用的先锋一词在命名的同时 ,也为我们更深入地把握某些艺术的本质设置了迷雾。不同的先锋艺术群落在表面上往往表现为具有相似特征的共同姿态 ,但其内在的价值取向却可能截然相反。比如朦胧诗与第三代诗歌。朦胧诗虽然在艺术表现手法上大量采用象征、变形、自由联想等手法 ,具有现代主义诗歌的特点 ,但理想与关怀依然是其主要的价值取向 ;而第三代诗歌尽管继承了朦胧诗的叛逆精神 ,但在价值取向上却大多走向了游戏与虚无     

李渔剧论的观众立场及其贡献

本文以为李渔戏剧理论的中心是观众 ,围绕观众来探讨剧本的创作、演出、戏剧的功能及其发展等是李渔剧论的最大特色。文章指出 :李渔从观众立场出发提出了“机趣”的戏剧功能观 ,并揭示了观众对戏剧艺术发展负有不可推卸的责任。     

合理产业结构的确定方法及预测

本文根据技术矩阵决定产业结构的思想,给出了不编制投入产出表年份的合理产业结构的计算方法及预测未来年份合理产业结构的计算方法。并将该方法应用于山东省合理产业结构的确定及预测。方法简便,易操作,且计算结果较理想。     

四个崭新的理论命题--论党的第三代中央领导集体对邓小平精神文明建设理论的新发展

党的第三代中央领导集体所标揭的四个崭新的理论命题,即文化是综合国力的重要标志;以人为本,重在素质;以立为本,重在建设;弘扬主旋律,提倡多样化,是对邓小平社会主义精神文明建设理论的新发展新贡献,不仅语言是新的,而且思维也是新的,典型地体现了党的第三代中央领导集体的理论创新品格。