On optimal testing for the equality of equicorrelation: An example of loss in power

Sen Gupta (1988) considered a locally most powerful (LMP) test for testing nonzero values of the equicorrelation coefficient of a standard symmetric multivariate normal distribution. This paper constructs analogous tests for the symmetric multivariate normal distribution. It shows that the new test is uniformly most powerful invariant even in the presence of a nuisance parameter, σ². Further applications of LMP invariant tests to several equicorrelated populations have been considered and an extension to panel data modeling has been suggested.     

基于B样条曲线的异常数据剔除与修复

文章针对大量复杂的靶场观测数据,通过构造初始拟合数据,利用B样条曲线的方法构造递推模型,使用基于样条平滑方法估计的判断门限对双向检验的结果数据是否异常进行判定,并且对满足修复条件的数据进行拟合修复,当双向检验的结果不同时,通过构造内推模型来进一步检验。实例分析表明:文章提出的方法相对其他方法能更有效地剔除异常数据,通过数据分段处理能更有效地检验那些可能产生阶段性跳跃的数据,使得模型具有更好的稳定性、更广的适用性和更高的异常数据剔除率。     

Testing for separability of spatial–temporal covariance functions

Most applications in spatial statistics involve modeling of complex spatial–temporal dependency structures, and many of the problems of space and time modeling can be overcome by using separable processes. This subclass of spatial–temporal processes has several advantages, including rapid fitting and simple extensions of many techniques developed and successfully used in time series and classical geostatistics. In particular, a major advantage of these processes is that the covariance matrix for a realization can be expressed as the Kronecker product of two smaller matrices that arise separately from the temporal and purely spatial processes, and hence its determinant and inverse are easily determinable. However, these separable models are not always realistic, and there are no formal tests for separability of general spatial–temporal processes. We present here a formal method to test for separability. Our approach can be also used to test for lack of stationarity of the process. The beauty of our approach is that by using spectral methods the mechanics of the test can be reduced to a simple two-factor analysis of variance (ANOVA) procedure. The approach we propose is based on only one realization of the spatial–temporal process.We apply the statistical methods proposed here to test for separability and stationarity of spatial–temporal ozone fields using data provided by the US Environmental Protection Agency (EPA).     

面板数据的聚类分析及其应用

 不同于传统的计量建模分析，本文探讨了多元统计方法在面板数据分析上的运用。文中介绍了面板数据的统计描述方法，构造了面板数据之间相似性的统计指标，并在此基础上提出了面板数据聚类分析的有效方法，通过实际应用取得了良好的效果。     

部分函数型线性变系数模型的序列相关检验

部分函数型线性变系数模型(PFLVCM)是近几年出现的一个比较灵活、应用广泛的新模型。在实际应用中,搜集到的经济和金融数据往往存在序列相关性。如果不考虑数据间的相关性直接对其进行建模,会影响模型中参数估计的精度和有效性。本文主要研究了PFLVCM中误差的序列相关性的检验问题,基于经验似然,把标量时间序列数据相关性检验的方法拓展到函数型数据中,提出了经验对数似然比检验统计量,并在零假设下得到了检验统计量的近似分布。通过蒙特卡洛数值模拟说明该统计量在有限样本下有良好的水平和功效。最后,把该方法用于检验美国商业用电消费数据是否有序列相关性,证明该统计量的有效性和实用性。     

A score test for overdispersion in Poisson regression based on the generalized Poisson-2 model

Overdispersion is a common phenomenon in Poisson modeling. The generalized Poisson (GP) regression model accommodates both overdispersion and underdispersion in count data modeling, and is an increasingly popular platform for modeling overdispersed count data. The Poisson model is one of the special cases in the collection of models which may be specified by GP regression. Thus, we may derive a test of overdispersion which compares the equi-dispersion Poisson model within the context of the more general GP regression model. The score test has an advantage over the likelihood ratio test (LRT) and over the Wald test in that the score test only requires that the parameter of interest be estimated under the null hypothesis (the Poisson model). Herein, we propose a score test for overdispersion based on the GP model (specifically the GP-2 model) and compare the power of the test with the LRT and Wald tests. A simulation study indicates the proposed score test based on asymptotic standard normal distribution is more appropriate in practical applications.     

系统性风险度量CoES的建模和检验

本文结合极值理论(Extreme Value Theory,EVT)和新的动态混合Copula(Dynamic Mixture Copula,DM-Copula)函数,提出了一种新的CoES估计方法DM-Copula-EVT。在EVT建模中,本文改进了阈值的选取方法以避免选择的主观性,并提出了一系列新的动态混合Copula以更好地刻画金融市场日益复杂的尾部关联性。此外,本文首次提出了检验CoES模型设定正确性的后验分析方法,包括无条件覆盖性检验和条件覆盖性检验。将本文建模和检验方法应用于我国金融市场,研究发现:相对于传统使用的t分布,EVT能更好地拟合指数的尾部分布;新的动态混合Copula函数能更好地刻画金融部门与系统之间的复杂关联性。     

Importance of sampling weights in multilevel modeling of international large-scale assessment data

Multilevel modeling is an important tool for analyzing large-scale assessment data. However, the standard multilevel modeling will typically give biased results for such complex survey data. This bias can be eliminated by introducing design weights which must be used carefully as they can affect the results. The aim of this paper is to examine different approaches and to give recommendations concerning handling design weights in multilevel models when analyzing large-scale assessments such as TIMSS (The Trends in International Mathematics and Science Study). To achieve the goal of the paper, we examined real data from two countries and included a simulation study. The analyses in the empirical study showed that using no weights or only level 1 weights sometimes could lead to misleading conclusions. The simulation study only showed small differences in estimation of the weighted and unweighted models when informative design weights were used. The use of unscaled or not rescaled weights however caused significant differences in some parameter estimates.     

On Small Samples Testing for Frailty Through Homogeneity Test

We derive a test in order to examine the need of modeling survival data using frailty models based on the likelihood ratio (LR) test for homogeneity. Test is developed for both complete and censored samples from a family of baseline distributions that satisfy a closure property. Approach motivated by I-divergence distance is used in order to determine “credible” regions for all parameters of baseline distribution for which homogeneity hypothesis is not rejected. Proposed test outperforms the usual asymptotic LR test both in very small samples with known frailty and for all small sample sizes under misspecified frailty.     

网络社区发现算法在流动表建模中的设计与应用

代际流动表可以统计子代与其父代社会地位配对数据的交互频数,反映了社会资源占有的优劣势在父子两代人之间的比较。对财富、阶级、特权等社会基本特征演变的实证考察,均依赖于代际流动表的量化分析。对数线性模型是流动表建模分析的基本工具,通过对列联表单元格频数进行拟合,可以识别流动表行分类与列分类之间的强弱交互效应,刻画父子社会地位间的交互结构。本文利用复杂网络社区发现算法分析父子社会地位的关联结构,针对简约对数线性模型拟合精度不够的问题,提出一种新的建模思路：利用社区发现算法对简约对数线性模型的残差列联表进行关联关系挖掘,将发现的社区效应作为附加参数约束引入原对数线性模型,以改善数据的拟合情况。由于该方法只在原简约对数线性模型中增加了一个参数约束,因此仍可以保证建模结果的简洁性及理论意义,同时社区效应补充了原对数线性模型对经验数据结构的解读。论文用此方法对来源于中国综合社会调查数据的经验代际职业流动表进行建模分析,较好地解释了子代职业阶层与父代职业阶层间的关联模式。     

Multiscale Adaptive Regression Models for Neuroimaging Data

Neuroimaging studies aim to analyze imaging data with complex spatial patterns in a large number of locations (called voxels) on a two-dimensional (2D) surface or in a 3D volume. Conventional analyses of imaging data include two sequential steps: spatially smoothing imaging data and then independently fitting a statistical model at each voxel. However, conventional analyses suffer from the same amount of smoothing throughout the whole image, the arbitrary choice of smoothing extent, and low statistical power in detecting spatial patterns. We propose a multiscale adaptive regression model (MARM) to integrate the propagation-separation (PS) approach (Polzehl and Spokoiny, 2000, 2006) with statistical modeling at each voxel for spatial and adaptive analysis of neuroimaging data from multiple subjects. MARM has three features: being spatial, being hierarchical, and being adaptive. We use a multiscale adaptive estimation and testing procedure (MAET) to utilize imaging observations from the neighboring voxels of the current voxel to adaptively calculate parameter estimates and test statistics. Theoretically, we establish consistency and asymptotic normality of the adaptive parameter estimates and the asymptotic distribution of the adaptive test statistics. Our simulation studies and real data analysis confirm that MARM significantly outperforms conventional analyses of imaging data.     

Test for randomness of the technology parameter in a stochastic frontier regression model

This paper considers the problem of testing for randomness of the technology parameter in a stochastic frontier regression model. A test statistic is proposed and its asymptotic distribution theory is discussed. Simulation results show that the proposed test maintains its level and also quite powerful against various alternatives. An empirical investigation has been carried out by applying the suggested test procedure to the data set on electric utility companies. The results are consistent with the general finding that the technology parameter of the stochastic frontier model used for modeling these data is random.     

Testing for the Presence of a Cure Fraction in Clustered Interval‐Censored Survival Data

Clustered interval‐censored survival data are often encountered in clinical and epidemiological studies due to geographic exposures and periodic visits of patients. When a nonnegligible cured proportion exists in the population, several authors in recent years have proposed to use mixture cure models incorporating random effects or frailties to analyze such complex data. However, the implementation of the mixture cure modeling approaches may be cumbersome. Interest then lies in determining whether or not it is necessary to adjust the cured proportion prior to the mixture cure analysis. This paper mainly focuses on the development of a score for testing the presence of cured subjects in clustered and interval‐censored survival data. Through simulation, we evaluate the sampling distribution and power behaviour of the score test. A bootstrap approach is further developed, leading to more accurate significance levels and greater power in small sample situations. We illustrate applications of the test using data sets from a smoking cessation study and a retrospective study of early breast cancer patients.     

Score test for testing zero-inflated Poisson regression against zero-inflated generalized Poisson alternatives

In several cases, count data often have excessive number of zero outcomes. This zero-inflated phenomenon is a specific cause of overdispersion, and zero-inflated Poisson regression model (ZIP) has been proposed for accommodating zero-inflated data. However, if the data continue to suggest additional overdispersion, zero-inflated negative binomial (ZINB) and zero-inflated generalized Poisson (ZIGP) regression models have been considered as alternatives. This study proposes the score test for testing ZIP regression model against ZIGP alternatives and proves that it is equal to the score test for testing ZIP regression model against ZINB alternatives. The advantage of using the score test over other alternative tests such as likelihood ratio and Wald is that the score test can be used to determine whether a more complex model is appropriate without fitting the more complex model. Applications of the proposed score test on several datasets are also illustrated.     

Semiparametric Negative Binomial Regression Models

Negative-binomial (NB) regression models have been widely used for analysis of count data displaying substantial overdispersion (extra-Poisson variation). However, no formal lack-of-fit tests for a postulated parametric model for a covariate effect have been proposed. Therefore, a flexible parametric procedure is used to model the covariate effect as a linear combination of fixed-knot cubic basis splines or B-splines. Within the proposed modeling framework, a log-likelihood ratio test is constructed to evaluate the adequacy of a postulated parametric form of the covariate effect. Simulation experiments are conducted to study the power performance of the proposed test.     

Lasso Regression Based on Empirical Mode Decomposition

The Hilbert–Huang transform uses the empirical mode decomposition (EMD) method to analyze nonlinear and nonstationary data. This method breaks a time series of data into several orthogonal sequences based on differences in frequency. These data components include the intrinsic mode functions (IMFs) and the final residue. Although IMFs have been used in the past as predictors for other variables, very little effort has been devoted to identifying the most effective predictors among IMFs. As lasso is a widely used method for feature selection within complex datasets, the main objective of this article is to present a lasso regression based on the EMD method for choosing decomposed components that exhibit the strongest effects. Both numerical experiments and empirical results show that the proposed modeling process can use time-frequency structure within data to reveal interactions between two variables. This allows for more accurate predictions concerning future events.     

Bayesian tests on components of the compound symmetry covariance matrix

Complex dependency structures are often conditionally modeled, where random effects parameters are used to specify the natural heterogeneity in the population. When interest is focused on the dependency structure, inferences can be made from a complex covariance matrix using a marginal modeling approach. In this marginal modeling framework, testing covariance parameters is not a boundary problem. Bayesian tests on covariance parameter(s) of the compound symmetry structure are proposed assuming multivariate normally distributed observations. Innovative proper prior distributions are introduced for the covariance components such that the positive definiteness of the (compound symmetry) covariance matrix is ensured. Furthermore, it is shown that the proposed priors on the covariance parameters lead to a balanced Bayes factor, in case of testing an inequality constrained hypothesis. As an illustration, the proposed Bayes factor is used for testing (non-)invariant intra-class correlations across different group types (public and Catholic schools), using the 1982 High School and Beyond survey data.     

On kernel machine learning for propensity score estimation under complex confounding structures

Post marketing data offer rich information and cost-effective resources for physicians and policy-makers to address some critical scientific questions in clinical practice. However, the complex confounding structures (e.g., nonlinear and nonadditive interactions) embedded in these observational data often pose major analytical challenges for proper analysis to draw valid conclusions. Furthermore, often made available as electronic health records (EHRs), these data are usually massive with hundreds of thousands observational records, which introduce additional computational challenges. In this paper, for comparative effectiveness analysis, we propose a statistically robust yet computationally efficient propensity score (PS) approach to adjust for the complex confounding structures. Specifically, we propose a kernel-based machine learning method for flexibly and robustly PS modeling to obtain valid PS estimation from observational data with complex confounding structures. The estimated propensity score is then used in the second stage analysis to obtain the consistent average treatment effect estimate. An empirical variance estimator based on the bootstrap is adopted. A split-and-merge algorithm is further developed to reduce the computational workload of the proposed method for big data, and to obtain a valid variance estimator of the average treatment effect estimate as a by-product. As shown by extensive numerical studies and an application to postoperative pain EHR data comparative effectiveness analysis, the proposed approach consistently outperforms other competing methods, demonstrating its practical utility.     

The glm log-rank test:general linear modeling of log-rank scores as a method of analysis for survival data

The use of general linear modeling (GLM) procedures based on log-rank scores is proposed for the analysis of survival data and compared to standard survival analysis procedures. For the comparison of two groups, this approach performed similarly to the traditional log-rank test. In the case of more complicated designs - without ties in the survival times - the approach was only marginally less powerful than tests from proportional hazards models, and clearly less powerful than a likelihood ratio test for a fully parametric model; however, with ties in the survival time, the approach proved more powerful than tests from Cox's semi-parametric proportional hazards procedure. The method appears to provide a reasonably powerful alternative for the analysis of survival data, is easily used in complicated study designs, avoids (semi-)parametric assumptions, and is quite computationally easy and inexpensive to employ.     

Bootstrap likelihood ratio test for Weibull mixture models fitted to grouped data

Abstract

Weibull mixture models are widely used in a variety of fields for modeling phenomena caused by heterogeneous sources. We focus on circumstances in which original observations are not available, and instead the data comes in the form of a grouping of the original observations. We illustrate EM algorithm for fitting Weibull mixture models for grouped data and propose a bootstrap likelihood ratio test (LRT) for determining the number of subpopulations in a mixture model. The effectiveness of the LRT methods are investigated via simulation. We illustrate the utility of these methods by applying them to two grouped data applications.