Bounds on dispersion of order statistics based on dependent symmetrically distributed random variables

We consider a fixed number of arbitrarily dependent random variables with a common symmetric marginal distribution. For each order statistic based on the variables, we determine a common optimal bound, dependent in a simple way on the sample size and number of order statistics, for various measures of dispersion of the order statistics, expressed in terms of the same dispersion measure of the single original variable. The dispersion measures are connected with the notion of M-functional of a random variable location with respect to a symmetric and convex loss function. The measure is defined as the expected loss paid for the discrepancy between the M-functional and the variable. The most popular examples are the median absolute deviation and variance.     

Testing the rate ratio under inverse sampling based on gradient statistic

Inverse sampling is widely applied in studies with dichotomous outcomes, especially when the subjects arrive sequentially or the response of interest is difficult to obtain. In this paper, we investigate the rate ratio test problem under inverse sampling based on gradient statistic with the asymptotic method and parametric bootstrap technique. The gradient statistic has many advantages, for example, it is simple to calculate and competitive with Wald-type, score and likelihood ratio tests in terms of local power. Numerical studies are carried out to evaluate the performance of our gradient test and the existing tests, namely Wald-type, score and likelihood ratio tests. The simulation results suggest that the gradient test based on the parametric bootstrap method has excellent type I error control and large powers even in small sample design. Two real examples, from a heart disease study and a drug comparison study, are applied to illustrate our methods.     

大学生党员思想和心理状况调查分析

以安徽大学为例,通过问卷调查的形式对大学生党员的思想和心理状况进行调查和分析,采用描述性统计和百分比同质性检验方法,得出大学生党员思想观念、思想政治教育、价值取向、入党动机等方面的表现情况。该调查分析有助于针对性地提高学校党建工作的质量和水平,也有助于加强对大学生党员的先进性教育和管理。     

On population‐based measures of agreement for binary classifications

The authors describe a model‐based kappa statistic for binary classifications which is interpretable in the same manner as Scott's pi and Cohen's kappa, yet does not suffer from the same flaws. They compare this statistic with the data‐driven and population‐based forms of Scott's pi in a population‐based setting where many raters and subjects are involved, and inference regarding the underlying diagnostic procedure is of interest. The authors show that Cohen's kappa and Scott's pi seriously underestimate agreement between experts classifying subjects for a rare disease; in contrast, the new statistic is robust to changes in prevalence. The performance of the three statistics is illustrated with simulations and prostate cancer data.     

Cluster analysis using different correlation coefficients

Partitioning objects into closely related groups that have different states allows to understand the underlying structure in the data set treated. Different kinds of similarity measure with clustering algorithms are commonly used to find an optimal clustering or closely akin to original clustering. Using shrinkage-based and rank-based correlation coefficients, which are known to be robust, the recovery level of six chosen clustering algorithms is evaluated using Rand’s C values. The recovery levels using weighted likelihood estimate of correlation coefficient are obtained and compared to the results from using those correlation coefficients in applying agglomerative clustering algorithms. This work was supported by RIC(R) grants from Traditional and Bio-Medical Research Center, Daejeon University (RRC04713, 2005) by ITEP in Republic of Korea.     

On the Ghoudi,Khoudraji, and Rivest test for extreme‐value dependence

Ghoudi, Khoudraji & Rivest [The Canadian Journal of Statistics 1998;26:187–197] showed how to test whether the dependence structure of a pair of continuous random variables is characterized by an extreme‐value copula. The test is based on a U‐statistic whose finite‐ and large‐sample variance are determined by the present authors. They propose estimates of this variance which they compare to the jackknife estimate of Ghoudi, Khoudraji & Rivest ( 1998 ) through simulations. They study the finite‐sample and asymptotic power of the test under various alternatives. They illustrate their approach using financial and geological data. The Canadian Journal of Statistics © 2009 Statistical Society of Canada     

Incomplete sufficient unbiased estimators in the problem of the nile

A family of incomplete sufficient unbiased esti¬mators is constructed for an arbitrary power of the parameter in the problem of the Nile. The variance is derived in a closed form and compared numerically with the mean square error of the maximum likelihood es t ima tor     

Modeling longitudinal binomial responses: implications from two dueling paradigms

The generalized estimating equations (GEEs) and generalized linear mixed-effects model (GLMM) are the two most popular paradigms to extend models for cross-sectional data to a longitudinal setting. Although the two approaches yield well-interpreted models for continuous outcomes, it is quite a different story when applied to binomial responses. We discuss major modeling differences between the GEE- and GLMM-derived models by presenting new results regarding the model-driven differences. Our results show that GLMM induces some artifacts in the marginal models at assessment times, making it inappropriate when applied to such responses from real study data. The different interpretations of parameters resulting from the conceptual difference between the two modeling approaches also carry quite significant implications and ramifications with respect to data and power analyses. Although a special case involving a scale difference in parameters between GEE and GLMM has been noted in the literature, its implications in real data analysis has not been thoroughly addressed. Further, this special case has a very limited covariate structure and does not apply to most real studies, especially multi-center clinical trials. The new results presented fill a substantial gap in the literature regarding the model-driven differences between the two dueling paradigms.     

Designing of a control chart using belief statistic for exponential distribution

A new control chart is proposed by using the belief statistic for the exponential distribution. The structure of the proposed control chart is given to measure the average run length for the shifted process. The comparison of the proposed chart is given with the existing charts in terms of the average run lengths, which shows the outperformance of the proposed chart. The performance of the proposed control chart is also discussed with the help of simulated data.     

Exact distribution of a modified Behrens–Fisher statistic

The exact distribution of a modified Behrens–Fisher statistic is derived. The distribution function is mostly elementary and is simpler than the exact distribution derived by Nel et al. Its practical use (including computationalefficiency and computational convenience) is discussed.