Corrected likelihood-ratio tests in logistic regression using small-sample data

Likelihood-ratio tests (LRTs) are often used for inferences on one or more logistic regression coefficients. Conventionally, for given parameters of interest, the nuisance parameters of the likelihood function are replaced by their maximum likelihood estimates. The new function created is called the profile likelihood function, and is used for inference from LRT. In small samples, LRT based on the profile likelihood does not follow χ² distribution. Several corrections have been proposed to improve LRT when used with small-sample data. Additionally, complete or quasi-complete separation is a common geometric feature for small-sample binary data. In this article, for small-sample binary data, we have derived explicitly the correction factors of LRT for models with and without separation, and proposed an algorithm to construct confidence intervals. We have investigated the performances of different LRT corrections, and the corresponding confidence intervals through simulations. Based on the simulation results, we propose an empirical rule of thumb on the use of these methods. Our simulation findings are also supported by real-world data.     

《汉语大字典》释义指瑕

《汉语大字典》中部分释义不当,失误原因有通假义失于辨察、义项表述有欠准确、例证时代欠晚、义项遗漏、引文注语和义项相违等。本文对此分类并加以质疑,逐一进行商榷补正。     

社区矫正犯罪控制功能论——以恢复性行刑为视角

社区矫正借助社会力量来控制犯罪,改变了以往国家单一的犯罪控制模式,实现了由一元向多元犯罪控制模式的转变。但囿于我国社区矫正法律规定的不完善,对社区矫正目标即改造罪犯的单一性认识,导致我国社区矫正犯罪控制功能难以有效发挥。为此,有必要以系统论为指导完善以社区矫正为中心的相关法律,以恢复性行刑为理念吸收包括被害人在内的其他社会人员参加社区矫正,充分发挥社区矫正犯罪控制之社会控制与法律控制功能。     

A note on the two-sample mean problem based on jackknife empirical likelihood

In this article, we employ the jackknife empirical likelihood (JEL) method to construct the confidence regions for the difference of the means of two d-dimensional samples. Compared with traditional EL for the two-sample mean problem, JEL is extremely simpler to use in practice and is more effective in computing. Based on the JEL ratio test, a version of Wilks’ theorem is developed. Furthermore, to improve the coverage accuracy of confidence regions, a Bartlett correction is applied. The effectiveness of the proposed method is demonstrated by a simulation study and a real data analysis.     

Bartlett-corrected two-sample adjusted empirical likelihood via resampling

To construct confidence regions for the difference of two population means, Liu and Yu (2010 Liu, Y., Yu, C.W. (2010). Bartlett correctable two-sample adjusted empirical likelihood. J. Multivariate Anal. 101(7):1701–1711.[Crossref], [Web of Science ®] , [Google Scholar]) proposed a two-sample adjusted empirical likelihood (AEL) with high-order precision. However, two issues have not been well addressed. The first one is that the AEL ratio function is bounded such that the size of the confidence regions may overly expand when the sample sizes are small and/or the dimension of data is large. The second issue is that its high-order precision relies on accurate estimation of the Bartlett factor, while accurately estimating the Bartlett factor is a serious challenge. In order to address these two problems simultaneously, we propose a two-sample modified AEL to ensure the boundedness of confidence regions and preserve the Bartlett correctability. A two-stage procedure is proposed for constructing accurate confidence regions via resampling. The finite-sample performance of the proposed method is illustrated by simulations and a real-data example.     

Hypothesis testing in log-Birnbaum-Saunders regressions

The log-Birnbaum-Saunders regression model introduced by Rieck and Nedelman (1991 Rieck, J. R., Nedelman, J. R. (1991). A log-linear model for the Birnbaum-Saunders distribution. Technometrics 33:51–60. [Google Scholar]) is useful for modeling lifetimes of materials and equipments subject to different conditions. Our goal in this article is twofold. First, we numerically evaluate the finite sample performances of the likelihood ratio, score and Wald tests in the log-Birnbaum-Saunders regression model. Second, we introduce a RESET-like misspecification test for that model. The null hypothesis is that the model is correctly specified which is tested against the alternative hypothesis of model misspecification. The power of the test is evaluated using Monte Carlo simulations. Bootstrap-based inference is also considered. An empirical application is presented and discussed.     

A unified approach to proving parametric bootstrap consistency for some goodness-of-fit tests

Because model misspecification can lead to inconsistent and inefficient estimators and invalid tests of hypotheses, testing for misspecification is critically important. We focus here on several general purpose goodness-of-fit tests which can be applied to assess the adequacy of a wide variety of parametric models without specifying an alternative model. Parametric bootstrap is the method of choice for computing the p-values of these tests however the proof of its consistency has never been rigourously shown in this setting. Using properties of locally asymptotically normal parametric models, we prove that under quite general conditions, the parametric bootstrap provides a consistent estimate of the null distribution of the statistics under investigation.     

中途之家的预防犯罪理论基础探析——以北京市朝阳区司法局阳光中途之家为例

中途之家是社区矫正模式之一,作为一种更为人道、文明的刑罚执行方式,在许多国家广泛应用。北京市朝阳区司法局创设了大陆首家中途之家。它有深厚的理论基础,在预防服刑人员重新犯罪方面发挥了非常重要的作用。中途之家的工作方案与刑法中个别预防理论,行为人中心主义、刑罚社会化学说以及刑罚人道观念中的预防犯罪思想和观点相契合,它们是中途之家创建的重要理论依据。     

On bootstrap testing inference in cure rate models

Survival models deal with the time until the occurrence of an event of interest. However, in some situations the event may not occur in part of the studied population. The fraction of the population that will never experience the event of interest is generally called cure rate. Models that consider this fact (cure rate models) have been extensively studied in the literature. Hypothesis testing on the parameters of these models can be performed based on likelihood ratio, gradient, score or Wald statistics. Critical values of these tests are obtained through approximations that are valid in large samples and may result in size distortion in small or moderate sample sizes. In this sense, this paper proposes bootstrap corrections to the four mentioned tests and bootstrap Bartlett correction for the likelihood ratio statistic in the Weibull promotion time model. Besides, we present an algorithm for bootstrap resampling when the data presents cure fraction and right censoring time (random and non-informative). Simulation studies are conducted to compare the finite sample performances of the corrected tests. The numerical evidence favours the corrected tests we propose. We also present an application in an actual data set.     

Accurate tests for the equality of coefficients of variation

ABSTRACT

A frequently encountered statistical problem is to determine if the variability among k populations is heterogeneous. If the populations are measured using different scales, comparing variances may not be appropriate. In this case, comparing coefficient of variation (CV) can be used because CV is unitless. In this paper, a non-parametric test is introduced to test whether the CVs from k populations are different. With the assumption that the populations are independent normally distributed, the Miller test, Feltz and Miller test, saddlepoint-based test, log likelihood ratio test and the proposed simulated Bartlett-corrected log likelihood ratio test are derived. Simulation results show the extreme accuracy of the simulated Bartlett-corrected log likelihood ratio test if the model is correctly specified. If the model is mis-specified and the sample size is small, the proposed test still gives good results. However, with a mis-specified model and large sample size, the non-parametric test is recommended.