Empirical likelihood confidence bands for distribution functions with missing responses

Distribution function estimation plays a significant role of foundation in statistics since the population distribution is always involved in statistical inference and is usually unknown. In this paper, we consider the estimation of the distribution function of a response variable Y with missing responses in the regression problems. It is proved that the augmented inverse probability weighted estimator converges weakly to a zero mean Gaussian process. A augmented inverse probability weighted empirical log-likelihood function is also defined. It is shown that the empirical log-likelihood converges weakly to the square of a Gaussian process with mean zero and variance one. We apply these results to the construction of Gaussian process approximation based confidence bands and empirical likelihood based confidence bands of the distribution function of Y. A simulation is conducted to evaluate the confidence bands.     

Comparison of causal effect estimators under exposure misclassification

Over the past decades, various principles for causal effect estimation have been proposed, all differing in terms of how they adjust for measured confounders: either via traditional regression adjustment, by adjusting for the expected exposure given those confounders (e.g., the propensity score), or by inversely weighting each subject's data by the likelihood of the observed exposure, given those confounders. When the exposure is measured with error, this raises the question whether these different estimation strategies might be differently affected and whether one of them is to be preferred for that reason. In this article, we investigate this by comparing inverse probability of treatment weighted (IPTW) estimators and doubly robust estimators for the exposure effect in linear marginal structural mean models (MSM) with G-estimators, propensity score (PS) adjusted estimators and ordinary least squares (OLS) estimators for the exposure effect in linear regression models. We find analytically that these estimators are equally affected when exposure misclassification is independent of the confounders, but not otherwise. Simulation studies reveal similar results for time-varying exposures and when the model of interest includes a logistic link.     

Fast and Stable Algorithms for Computing and Sampling From the Noncentral Hypergeometric Distribution

Although the noncentral hypergeometric distribution underlies conditional inference for 2 × 2 tables, major statistical packages lack support for this distribution. This article introduces fast and stable algorithms for computing the noncentral hypergeometric distribution and for sampling from it. The algorithms avoid the expensive and explosive combinatorial numbers by using a recursive relation. The algorithms also take advantage of the sharp concentration of the distribution around its mode to save computing time. A modified inverse method substantially reduces the number of searches in generating a random deviate. The algorithms are implemented in a Java class, Hypergeometric, available on the World Wide Web.     

On the asymptotic power and relative efficiency of the frequency X2 test

The asymptotic (Pitman) power of the X² test is investigated for particular classes of alternatives. A simple rule is introduced to identify ‘orthogonal alternatives’, for which the noncentrality parameter can be computed in a very simple way. In the sequel, restricted alternatives are considered and the ARE of the unrestricted test w.r.t. the restricted one is shown to depend only on the numbers of degrees of freedom. The concluding section discusses ‘undetectable alternatives’, i.e. alternatives for which the noncentrality vanishes.     

矩阵方程与Cramer法则的推广

本文讨论了矩阵方程AXB=C(A,B可逆)的用行列式表示的求解公式,然后指出它是Cramer法则的重要推广.     

Bayesian Multivariate Spatial Interpolation with Data Missing by Design

In a network of s _g sites, responses like levels of airborne pollutant concentrations may be monitored over time. The sites need not all measure the same set of response items and unmeasured items are considered as data missing by design . We propose a hierarchical Bayesian approach to interpolate the levels of, say, k responses at s _u other locations called ungauged sites and also the unmeasured levels of the k responses at the gauged sites. Our method involves two steps. First, when all hyperparameters are assumed to be known, a predictive distribution is derived. In turn, an interpolator, its variance and a simultaneous interpolation region are obtained. In step two, we propose the use of an empirical Bayesian approach to estimate the hyperparameters through an EM algorithm. We base our theory on a linear Gaussian model and the relationship between a multivariate normal and matrix T -distribution. Our theory allows us to pool data from several existing networks that measure different subsets of response items for interpolation.     

矩阵管理模式在高校图书馆阅读推广团队建设中的应用

矩阵管理是指为完成某项特定工作任务而形成的工作小组的管理模式。应用矩阵管理模式加强高校图书馆阅读推广团队建设,应注意把好团队负责人选择关,明确团队管理流程和成员的任务要求,注重各业务点的工作量均衡,促进各业务环节的配合,同时优化绩效评估方式,建立阅读推广活动评价和奖惩机制。     

基于矩阵打分值和化学位移值预测酶蛋白质中β-发夹模体

酶是一类具有催化功能的蛋白质,对其结构和功能的研究是非常有必要的。特殊模体β-发夹是一种简单的超二级结构,它们包含了丰富的折叠信息,对酶中β-发夹的预测有助于酶结构和功能的预测。本文建立了非冗余的β-发夹模体数据集,包含1080条酶蛋白质链,2818个β-发夹模体,1098个非β-发夹。提取位点亲疏水组分及位点亲疏水紧邻关联组分作为参数,运用矩阵打分算法得到的预测结果不理想。将位点亲疏水、位点亲疏水紧邻关联组分为参数得到的打分值和平均化学位移值共同作为特征参数,输入支持向量机算法对模体进行预测,5交叉检验预测总精度是81.8%,相关系数达到了0.636。     

A multiple model discrimination procedure

The case of selecting between a set of fixed models is considered. The true model is assumed to be contained in the set of proposed models and errors are taken to be normally distributed. A sequential procedure which yeilds probabilities of incorrect selections is proposed. The procedure is shown to have optimal properties and is extended to the estimated model case by a bootstrap procedure.