Asymptotic expansions for the ability estimator in item response theory

Asymptotic approximations to the distributions of the ability estimator and its transformations in item response theory are derived beyond the usual normal one when associated item parameters are given as in tailored testing. For the approximations, the asymptotic cumulants of the estimators up to the fourth order with the higher-order asymptotic variances are obtained under possible model misspecification. For testing and interval estimation of abilities, the asymptotic cumulants of the pivots studentized in four ways are derived. Numerical examples with simulations including those for confidence intervals for abilities are given using the three-parameter logistic model.     

一类具有Allee影响的捕食者-食饵扩散系统研究

讨论一类具有Allee影响的捕食者-食饵扩散模型解的整体性态.通过线性化方法和Lyapunov泛函方法分别证明了该模型正平衡点的局部渐近稳定性和全局渐近稳定性.     

Asymptotic cumulants of the parameter estimators in item response theory

The asymptotic cumulants of the parameter estimators for the three-parameter logistic model in item response theory are derived up to the fourth order with the higher-order added asymptotic variances. The asymptotic cumulants of the corresponding Studentized estimators up to the third order are also given. The estimators are obtained by marginal maximum likelihood using the standard normal distribution for the latent variable with and without model misspecification. Numerical examples with fixed guessing parameters show advantages of the asymptotic expansions over the usual normal approximation. This work was partially supported by Grant-in-Aid for Scientific Research from the Japanese Ministry of Education, Culture, Sports, Science and Technology.     

The asymptotic validity of invariant procedures for the repeated measures model and multivariate linear model

Fairly general sufficient conditions are given to guarantee that invariant tests about means in the multivariate linear model and the repeated measures model have the correct asymptotic size when the normal assumption under which the tests are derived is relaxed. These conditions are the same as Huber's condition which guarantees asymptotic validity of the size of the F-test for the univariate linear model.     

Asymptotic properties of the Bayes modal estimators of item parameters in item response theory

Asymptotic cumulants of the Bayes modal estimators of item parameters using marginal likelihood in item response theory are derived up to the fourth order with added higher-order asymptotic variances under possible model misspecification. Among them, only the first asymptotic cumulant and the higher-order asymptotic variance for an estimator are different from those by maximum likelihood. Corresponding results for studentized Bayes estimators and asymptotically bias-corrected ones are also obtained. It was found that all the asymptotic cumulants of the bias-corrected Bayes estimator up to the fourth order and the higher-order asymptotic variance are identical to those by maximum likelihood with bias correction. Numerical illustrations are given with simulations in the case when the 2-parameter logistic model holds. In the numerical illustrations, the maximum likelihood and Bayes estimators are used, where the same independent log-normal priors are employed for discriminant parameters and the hierarchical model is adopted for the prior of difficulty parameters.     

一类两参数半线性奇摄动问题解的渐近性态

本文研究了一类两参数半线性奇摄动问题的基本模型.利用奇摄动方法,对该问题解的结构在两个小参数相互关联的三种不同情形下作了讨论.得到了该问题在三种不同情形下的渐近解并证明了在三种情形下解的结构与渐近性态.     

一类两参数非线性奇摄动边值问题解的渐近性态

本文研究了一类两参数非线性奇摄动边值问题的基本模型.利用奇摄动方法,对该问题解的结构在两个小参数相互关联的三种不同情形下作了讨论,得到了该问题的渐近解并证明了在三种情形下不同的解的结构与渐近性态.     

Linear relations in time series models. II

In this paper an asymptotic theory is developed for a new time series model which was introduced in a previous paper [5]. An algorithm for computing estimates of the parameters of this time series model is given, and it is shown that these estimators are asymptotically efficient in the sense that they have the same asymptotic distribution as the maximum likelihood estimators.     

Stability properties and Hopf bifurcation of a delayed viral infection model with lytic immune response

A class of more general delayed viral infection model with lytic immune response is proposed based on some important biological meanings. The effect of time delay on stabilities of the equilibria is given. The sufficient criteria for local and global asymptotic stabilities of the viral free equilibrium and the local asymptotic stabilities of the no-immune response equilibrium are given. We also get the sufficient criteria for stability switch of the positive equilibrium. Numerical simulations are carried out to explain the mathematical conclusions.     

基于纵向数据的Poisson-Gamma模型系数的随机性检验

应用随机系数化方法对纵向数据的Poisson-Gamma回归模型进行了研究,采用Laplace展开方法得到了关于响应变量的近似似然函数并得到模型系数的随机性检验的Score统计量.通过Monte Carlo模拟分析了检验的渐近功效.最后把得到的检验统计量应用到具体的数值实例分析中说明其有效性.     

Asymptotic periodicity of a food-limited diffusive population model with time-delay

In this paper, a general reaction-diffusion food-limited population model with time-delay is proposed. Accordingly, the existence and uniqueness of the periodic solutions for the boundary value problem and the asymptotic periodicity of the initial-boundary value problem are considered. Finally, the effect of the time-delay on the asymptotic behavior of the solutions is given.     

利用样本分位数的Logistic分布参数的渐近置信估计

基于Logistic分布的若干个样本分位数 ,利用线性回归模型建立Logistic分布位置参数及尺度参数的渐近正态且渐近无偏估计量 ,得到分布参数的渐近置信估计。     

微分方程零解的弱渐近稳定与不稳定的判定定理

给出了平凡解弱渐近稳定定义及在已知导函数 d Vdt负定的情况下 ,通过 V( t,x)函数的符号性质来判定微分方程平凡解的弱渐近稳定性与不稳定性 ,并举例说明定理的应用 .     

Asymptotic normality of estimating risk upon the wavelet-vaguelette decomposition of a signal function in a model with correlated noise

The problem of estimating the function when using a homogeneous linear operator in a model with correlated noise is considered. The asymptotic properties of estimating risk upon the threshold wavelet-vaguelette decomposition of a signal are studied. The conditions under which the asymptotic normality of an unbiased risk estimate holds are given.     

Asymptotic Properties of a Nonparametric Regression Function Estimator with Randomly Truncated Data

In this paper, we define a new kernel estimator of the regression function under a left truncation model. We establish the pointwise and uniform strong consistency over a compact set and give a rate of convergence of the estimate. The pointwise asymptotic normality of the estimate is also given. Some simulations are given to show the asymptotic behavior of the estimate in different cases. The distribution function and the covariable’s density are also estimated.     

Global Qualitative Analysis for a Ratio-Dependent Predator-Prey Model with Delay

A ratio-dependent predator-prey model with time lag for predator is proposed and analyzed. Mathematical analyses of the model equations with regard to boundedness of solutions, nature of equilibria, permanence, and stability are analyzed. We note that for a ratio-dependent system local asymptotic stability of the positive steady state does not even guarantee the so-called persistence of the system and, therefore, does not imply global asymptotic stability. It is found that an orbitally asymptotically stable periodic orbit exists in that model. Some sufficient conditions which guarantee the global stability of positive equilibrium are given.     

General projection-pursuit estimators for the common principal components model: influence functions and Monte Carlo study

The common principal components (CPC) model for several groups of multivariate observations assumes equal principal axes but possibly different variances along these axes among the groups. Under a CPCs model, generalized projection-pursuit estimators are defined by using score functions on the dispersion measure considered. Their partial influence functions are obtained and asymptotic variances are derived from them. When the score function is taken equal to the logarithm, it is shown that, under a proportionality model, the eigenvector estimators are optimal in the sense of minimizing the asymptotic variance of the eigenvectors, for a given scale measure.     

关于渐近循环马氏链泛函的强大数定律

研究了一类非齐次马氏链———渐近循环马氏链泛函的强大数定律,首先引出了渐近循环马氏链的概念,然后给出了若干引理.利用了渐近循环马氏链关于状态序偶出现频率的强大数定理给出并证明了关于渐近循环马氏链泛函的强大数定律,所得定理作为推论可得到已有的结果.     

Asymptotic distribution of the weighted least squares estimator

This paper derives the asymptotic distribution of the weighted least squares estimator (WLSE) in a heteroscedastic linear regression model. A consistent estimator of the asymptotic covariance matrix of the WLSE is also obtained. The results are obtained under weak conditions on the design matrix and some moment conditions on the error distributions. It is shown that most of the error distributions encountered in practice satisfy these moment conditions. Some examples of the asymptotic covariance matrices are also given.     

弹性-应变软化粘塑性材料反平面剪切动态扩展裂纹尖端的渐近解*

本文首先给出了一种用于描述材料软化,并存在有粘塑性的材料模型.用这种模型对反平面剪切型动态扩展状态下,裂纹尖端的弹粘塑性场进行了渐近分析,给出了弹性－应变软化粘塑性材料反平面剪切动态扩展裂纹尖端的渐近解方程.分析结果表明,在裂纹尖端应变具有(ln(R/r))1/(n＋1)的奇异性,应力具有(ln(R/r))-n/(n＋1)的奇异性.从而本文揭示了应变软化粘塑性材料反平面剪切动态扩展裂纹尖端的渐近行为.