Asymptotic approximations to the distribution of Kendall's sample τ

This paper provides a saddlepoint approximation to the distribution of the sample version of Kendall's τ, which is a measure of association between two samples. The saddlepoint approximation is compared with the Edgeworth and the normal approximations, and with the bootstrap resampling distribution. A numerical study shows that with small sample sizes the saddlepoint approximation outperforms both the normal and the Edgeworth approximations. This paper gives also an analytical comparison between approximated and exact cumulants of the sample Kendall's τ when the two samples are independent.     

Predictive Hierarchic Modeling of Operational Characteristics in Clinical Trials

An analytic methodology for patient enrollment modeling using a Poisson-gamma model is developed by Anisimov & Fedorov (2005–2007). For modeling hierarchic processes associated with enrollment, a new methodology using evolving stochastic processes is proposed. This provides rather general and unified framework to describe various operational processes associated with enrollment. The technique for calculating predictive distributions, mean, and credibility bounds for evolving processes is developed. Some applications to modeling operational characteristics in clinical trials are considered with focus to modeling events associated with incoming and follow-up patients in different settings. For these models, predictive characteristics are derived in a closed form.     

A general approximation to quantiles

For many continuous distributions, a closed-form expression for their quantiles does not exist. Numerical approximations for their quantiles are developed on a distribution-by-distribution basis. This work develops a general approximation for quantiles using the Taylor expansion. Our method only requires that the distribution has a continuous probability density function and its derivatives can be derived to a certain order (usually 3 or 4). We demonstrate our unified approach by approximating the quantiles of the normal, exponential, and chi-square distributions. The approximation works well for these distributions.     

科学确定职业院校招生规模的方法研究

在研究职业教育城乡一体化的过程中,课题组研究探讨出一套根据一个地区或一个职业院校的教育资源合理确定这一地区或者这一学校的招生规模,达到充分利用教育资源,获得最好的教育效益和经济效益的各种定量方法,从而为教育管理部门和职业院校运用数学和经济学理论合理确定招生规模提供参考。     

Sums of powers of binomial coefficients

An asymptotic series for sums of powers of binomial coefficients is derived, the general term being defined and usable with a computer symbolic language. Sums of squares of coefficients in the symmetric case are shown to have a link with classical moment problems, but this property breaks down for cubes and higher powers. Problems of remainders for the asymptotic series are mentioned. Using the reflection formula for I'(.), a continuous form for a binomial function is set up, and this becomes oscillatory outstde the usual range. A new contmued fraction emerges for the logarithm of an adjusted sum of binomial squares. The note is a contribution to the problem of the interpretation of asymptotic series and processes for their convergence acceleration.     

Cumulants of random sum distributions

Consider a random variable S being the sum of a number N of independent and identically distributed random variables X_j (j = 1, 2, ...) where the number N is itself a non-negative integer-valued random variable independent of the X_j An explicit expression of the r-th cumulant of S is given in terms of the cumulants of N and X_j, Asymptotic properties of the distribution of S are also discussed.     

“90后”大学生入学教育新模式探索

高校应针对"90后"大学生的特点及独特的个性,探索新的教育途径和方法。     

中国居民代际收入流动性的变化趋势及影响机制研究

基于1989~2015年共计10轮CHNS数据,本文采用代际收入弹性和代际收入秩关联系数双重测度指标对我国居民代际收入流动性进行了测算,发现代际收入流动性在1991~2004年期间基本保持稳定,2004年以后呈现出不断上升的变化趋势。基于收入分组视角的研究发现,各收入组2004年以后代际收入阶层固化程度均有所降低,但高收入组和低收入组的固化程度远高于其他各组,中等收入群体是目前我国保持较高代际收入流动性的主要动力来源。从城乡差异视角看,受大规模农村劳动力向城镇流动的影响,2000年后农村家庭的代际流动性显著提升,且持续高于城市居民的代际流动性。进一步,基于人力资本分析框架对我国代际收入传递机制进行了探究,发现父亲的非教育因素在代际收入传递中起到主导作用。受整体社会制度环境不断改善的积极影响,2004年以后非教育传递机制不断减弱,对代际收入流动性的提升起到较大助推作用;而受高等教育扩张政策的影响,教育因素在2004年左右一定程度上削弱了代际收入流动性。     

A Note on the Large Sample Properties of Estimators Based on Generalized Linear Models for Correlated Pseudo‐observations

Pseudo‐values have proven very useful in censored data analysis in complex settings such as multi‐state models. It was originally suggested by Andersen et al., Biometrika, 90, 2003, 335 who also suggested to estimate standard errors using classical generalized estimating equation results. These results were studied more formally in Graw et al., Lifetime Data Anal., 15, 2009, 241 that derived some key results based on a second‐order von Mises expansion. However, results concerning large sample properties of estimates based on regression models for pseudo‐values still seem unclear. In this paper, we study these large sample properties in the simple setting of survival probabilities and show that the estimating function can be written as a U‐statistic of second order giving rise to an additional term that does not vanish asymptotically. We further show that previously advocated standard error estimates will typically be too large, although in many practical applications the difference will be of minor importance. We show how to estimate correctly the variability of the estimator. This is further studied in some simulation studies.     

高校扩招与城市发展

高校扩招已成为社会和教育界讨论的热点问题。全面认识高校扩招与城市发展之间的相互关系,对于城市建设与高校发展都具有十分重要的作用。高校扩招与城市发展具有正相关性,城市发展为高校扩招提供了市场需求,高校扩招是促进城市发展的重要途径。本文从城市发展的角度,给出了高校扩招后的建议,提出了大力发展应用型大学的必要性。