Confidence interval estimation and hypothesis testing for a common correlation coefficient

Several procedures have been proposed for testing the hypothesis that all off-diagonal elements of the correlation matrix of a multivariate normal distribution are equal. If the hypothesis of equal correlation can be accepted, it is then of interest to estimate and perhaps test hypotheses for the common correlation. In this paper, two versions of five different test statistics are compared via simulation in terms of adequacy of the normal approximation, coverage probabilities of confidence intervals, control of Type I error, and power. The results indicate that two test statistics based on the average of the Fisher z-transforms of the sample correlations should be used in most cases. A statistic based on the sample eigenvalues also gives reasonable results for confidence intervals and lower-tailed tests.     

Generalized information matrix tests for copulas

We propose a family of goodness-of-fit tests for copulas. The tests use generalizations of the information matrix (IM) equality of White and so relate to the copula test proposed by Huang and Prokhorov. The idea is that eigenspectrum-based statements of the IM equality reduce the degrees of freedom of the test’s asymptotic distribution and lead to better size-power properties, even in high dimensions. The gains are especially pronounced for vine copulas, where additional benefits come from simplifications of score functions and the Hessian. We derive the asymptotic distribution of the generalized tests, accounting for the nonparametric estimation of the marginals and apply a parametric bootstrap procedure, valid when asymptotic critical values are inaccurate. In Monte Carlo simulations, we study the behavior of the new tests, compare them with several Cramer–von Mises type tests and confirm the desired properties of the new tests in high dimensions.     

An algorithmic approach to construct D-optimal saturated designs for logistic model

In this paper, locally D-optimal saturated designs for a logistic model with one and two continuous input variables have been constructed by modifying the famous Fedorov exchange algorithm. A saturated design not only ensures the minimum number of runs in the design but also simplifies the row exchange computation. The basic idea is to exchange a design point with a point from the design space. The algorithm performs the best row exchange between design points and points form a candidate set representing the design space. Naturally, the resultant designs depend on the candidate set. For gain in precision, intuitively a candidate set with a larger number of points and the low discrepancy is desirable, but it increases the computational cost. Apart from the modification in row exchange computation, we propose implementing the algorithm in two stages. Initially, construct a design with a candidate set of affordable size and then later generate a new candidate set around the points of design searched in the former stage. In order to validate the optimality of constructed designs, we have used the general equivalence theorem. Algorithms for the construction of optimal designs have been implemented by developing suitable codes in R.     

Quasi-minimax estimation in the partial linear model

This article discusses the minimax estimator in partial linear model y = Zβ + f + ε under ellipsoidal restrictions on the parameter space and quadratic loss function. The superiority of the minimax estimator over the two-step estimator is studied in the mean squared error matrix criterion.     

Numerical evaluation of tests based on different heteroskedasticity-consistent covariance matrix estimators

This article considers the issue of performing tests in linear heteroskedastic models when the test statistic employs a consistent variance estimator. Several different estimators are considered, namely: HC0, HC1, HC2, HC3, and their bias-adjusted versions. The numerical evaluation is performed using numerical integration methods; the Imhof algorithm is used to that end. The results show that bias-adjustment of variance estimators used to construct test statistics delivers more reliable tests when they are performed for the HC0 and HC1 estimators, but the same does not hold for the HC3 estimator. Overall, the most reliable test is the HC3-based one.     

Symmetrical design for symmetrical global sensitivity analysis of model output

Symmetrical global sensitivity analysis (SGSA) can help practitioners focusing on the symmetrical terms of inputs whose uncertainties have an impact on the model output, which allows reducing the complexity of the model. However, there remains the challenging problem of finding an efficient method to get symmetrical global sensitivity indices (SGSI) when the functional form of the symmetrical terms is unknown, including numerical and non-parametric situations. In this study, we propose a novel sampling plan, called symmetrical design, for SGSA. As a preliminary experiment for model feature extracting, such plan offers the virtue of run-size economy due to its closure respective to the given group. Using the design, we give estimation methods of SGSI as well as their asymptotic properties respectively for numerical model and non-parametrical model directly by the model outputs, and further propose a significance test for SGSI in non-parametric situation. A case study for a benchmark of GSA and a real data analysis show the effectiveness of the proposed design.     

A New Feature Selection Method for Text Categorization of Customer Reviews

With the rapid development of e-commerce, online consumer review plays an increasingly important role in consumers’ purchase decisions. Most research papers use the quantitative measures of consumer reviews for statistical analysis. Here we focus on analyzing the texts of customer reviews with text mining tools. We propose a new feature selection method called maximizing the difference. Various classification methods such as boosting, random forest and SVM are used to test the performance of the new method along with different evaluation criteria. Both simulation and empirical results show that it improves the effectiveness of the classifier over the existing methods.     

Modified linear discriminant analysis using block covariance matrix in high-dimensional data

Among many classification methods, linear discriminant analysis (LDA) is a favored tool due to its simplicity, robustness, and predictive accuracy but when the number of genes is larger than the number of observations, it cannot be applied directly because the within-class covariance matrix is singular. Also, diagonal LDA (DLDA) is a simpler model compared to LDA and has better performance in some cases. However, in reality, DLDA requires a strong assumption based on mutual independence. In this article, we propose the modified LDA (MLDA). MLDA is based on independence, but uses the information that has an effect on classification performance with the dependence structure. We suggest two approaches. One is the case of using gene rank. The other involves no use of gene rank. We found that MLDA has better performance than LDA, DLDA, or K-nearest neighborhood and is comparable with support vector machines in real data analysis and the simulation study.     

社会化网络3维用户界面设计分析与研究

为了寻找三维用户界面设计策略，在归纳2维（2D）与2．5维（2．5D）用户界面包含的内容与设计策略的基础上，从3维（3D）用户界面的交互任务、信息呈现和用户搜索行为三方面进行了分析，整合了用户需求、空间行为、空间任务，创新性地构建了面向真3D空间的“需求-任务-层次模型”，为3D用户界面的构建提供了新的思路。此外，从细节层面对3D用户界面具体设计原则进行分析，提出了“信息呈现设计矩阵”，对3D用户界面设计具有一定的指导意义。