Testing equality of two normal covariance matrices with monotone missing data

Abstract

The problem of testing equality of two multivariate normal covariance matrices is considered. Assuming that the incomplete data are of monotone pattern, a quantity similar to the Likelihood Ratio Test Statistic is proposed. A satisfactory approximation to the distribution of the quantity is derived. Hypothesis testing based on the approximate distribution is outlined. The merits of the test are investigated using Monte Carlo simulation. Monte Carlo studies indicate that the test is very satisfactory even for moderately small samples. The proposed methods are illustrated using an example.     

Heteroscedastic Global Tests that the Regression Parameters for Two or More Independent Groups are Identical

Simulation results are reported on methods that allow both within group and between group heteroscedasticity when testing the hypothesis that independent groups have identical regression parameters. The methods are based on a combination of extant techniques, but their finite-sample properties have not been studied. Included are results on the impact of removing all leverage points or just bad leverage points. The method used to identify leverage points can be important and can improve control over the Type I error probability. Results are illustrated using data from the Well Elderly II study.     

Computing maximum likelihood estimates from type II doubly censored exponential data

It is well-known that, under Type II double censoring, the maximum likelihood (ML) estimators of the location and scale parameters, θ and δ, of a twoparameter exponential distribution are linear functions of the order statistics. In contrast, when θ is known, theML estimator of δ does not admit a closed form expression. It is shown, however, that theML estimator of the scale parameter exists and is unique. Moreover, it has good large-sample properties. In addition, sharp lower and upper bounds for this estimator are provided, which can serve as starting points for iterative interpolation methods such as regula falsi. Explicit expressions for the expected Fisher information and Cramér-Rao lower bound are also derived. In the Bayesian context, assuming an inverted gamma prior on δ, the uniqueness, boundedness and asymptotics of the highest posterior density estimator of δ can be deduced in a similar way. Finally, an illustrative example is included.     

Estimator Choice and Fisher's Paradox: A Monte Carlo Study

This paper argues that Fisher's paradox can be explained away in terms of estimator choice. We analyse by means of Monte Carlo experiments the small sample properties of a large set of estimators (including virtually all available single-equation estimators), and compute the critical values based on the empirical distributions of the t-statistics, for a variety of Data Generation Processes (DGPs), allowing for structural breaks, ARCH effects etc. We show that precisely the estimators most commonly used in the literature, namely OLS, Dynamic OLS (DOLS) and non-prewhitened FMLS, have the worst performance in small samples, and produce rejections of the Fisher hypothesis. If one employs the estimators with the most desirable properties (i.e., the smallest downward bias and the minimum shift in the distribution of the associated t-statistics), or if one uses the empirical critical values, the evidence based on US data is strongly supportive of the Fisher relation, consistently with many theoretical models.     

Divergence-based estimation and testing with misclassified data

The well-known chi-squared goodness-of-fit test for a multinomial distribution is generally biased when the observations are subject to misclassification. In Pardo and Zografos (2000) the problem was considered using a double sampling scheme and ø-divergence test statistics. A new problem appears if the null hypothesis is not simple because it is necessary to give estimators for the unknown parameters. In this paper the minimum ø-divergence estimators are considered and some of their properties are established. The proposed ø-divergence test statistics are obtained by calculating ø-divergences between probability density functions and by replacing parameters by their minimum ø-divergence estimators in the derived expressions. Asymptotic distributions of the new test statistics are also obtained. The testing procedure is illustrated with an example.     

治安管理处罚方式的新发展

处罚方式是关于具体的处罚手段与类型的法律规定,在治安管理处罚中具有非常重要的作用。随着社会主体多元化,社会关系复杂化,治安管理处罚方式必然要多样化。国外的社区矫正制度尤其值得借鉴。     

Assessing accuracy of a continuous screening test in the presence of verification bias

Summary.  In studies to assess the accuracy of a screening test, often definitive disease assessment is too invasive or expensive to be ascertained on all the study subjects. Although it may be more ethical or cost effective to ascertain the true disease status with a higher rate in study subjects where the screening test or additional information is suggestive of disease, estimates of accuracy can be biased in a study with such a design. This bias is known as verification bias. Verification bias correction methods that accommodate screening tests with binary or ordinal responses have been developed; however, no verification bias correction methods exist for tests with continuous results. We propose and compare imputation and reweighting bias-corrected estimators of true and false positive rates, receiver operating characteristic curves and area under the receiver operating characteristic curve for continuous tests. Distribution theory and simulation studies are used to compare the proposed estimators with respect to bias, relative efficiency and robustness to model misspecification. The bias correction estimators proposed are applied to data from a study of screening tests for neonatal hearing loss.     

湖南省省属高校经常性财政拨款新模式构建研究

经过近几年来高校管理体制的大幅度调整变化,目前湖南省省属高校所采用的经常性财政拨款方案已不能适应新形式的需要。成为适时之需,构建一种公平合理、简单有效的新模式,既发挥财政拨款在高教事业中的基础作用,又引导高校不断提高办学效益。     

我国中等收入群体比重及其特征

中等收入群体的界定标准、规模和特征一直是学术界关注的焦点。在回顾和评述现有各种界定标准的基础上,建议采用全球所有国家收入中位数的67%~200%作为定义我国中等收入群体的上下限。研究发现,近些年我国中等收入群体比重在逐渐提高,从2002年的10%上升到2016年的28.9%,这主要源于我国居民整体收入水平的提高而不是收入分配格局的变化。要扩大我国中等收入群体比重,保持中高速增长至关重要,政策的重点是提“低”而不是限“高”,同时要防范现有的中等收入群体跌落为低收入群体。中等收入群体主要分布在城市地区,收入来源主要是工资性收入,储蓄率偏高,受教育水平明显高于低收入者和贫困人口。中等收入群体的标准下限附近分布着规模客观的低收入者,他们是扩大中等收入者比重的潜在来源,应是政策瞄准的主要对象。     

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.