含结构零2×2表中风险比齐性检验的样本量研究

本文研究了在临床和流行病学中出现的K个独立含结构零的2×2列联表.利用风险比推导出基于Wald型,基于对数变换型以及基于Score型的三个检验统计量,以检验层间齐性假设,获得了分别基于这三个检验统计量的控制功效的样本量公式和数值实验结果.模拟研究表明基于Score检验和基于对数变换检验的样本量公式比基于Wald检验的样本量公式更精确,更能有效保证预先给定的功效.推广了基于列联表问题的假设检验方法.     

一类函数的对数完全单调性

通过对参数λ,μ的讨论,主要利用函数的单调性理论,已有对数完全单调函数的性质以及幂函数的积分表达式研究了函数Gλ,μ(x)及函数[Gλ,μ(x)]-1的对数完全单调性,并在此基础上得到了一定条件下函数Gλ,μ(x)及[Gλ,μ(x)]-1对数完全单调的充要条件.     

双对数模型对模型模拟误差的放缩问题探讨

对双对数模型lg Y=a0+a1lg X1+a2lg X2+…+anlg Xn与其对应的指数模型y=c0xa11xa22…xann的模拟相对误差的关系进行了探讨,指出双对数模型具有放大和缩小指数模型相对误差的特性.对二者的关系进行了理论推导和实例验证,并给出了二者的定量关系式.     

Lemniscates and inequalities for the logarithmic capacities of continua

It is shown that if P(z) = z ⁿ + ? is a polynomial with connected lemniscate E(P) = {z: ¦P(z)¦ ≤ 1} and m critical points, then, for any n? m+1 points on the lemniscate E(P), there exists a continuum γ ? E(P) of logarithmic capacity cap γ ≤ 2^?1/n which contains these points and all zeros and critical points of the polynomial. As corollaries, estimates for continua of minimum capacity containing given points are obtained.     

Asymptotic results for weighted means of linear combinations of independent Poisson random variables

ABSTRACT

In this paper we prove the large deviation principle for a class of weighted means of linear combinations of independent Poisson distributed random variables, which converge weakly to a normal distribution. The interest in these linear combinations is motivated by the diffusion approximation in Lansky [On approximations of Stein's neuronal model, J. Theoret. Biol. 107 (1984), pp. 631–647] of the Stein's neuronal model (see Stein [A theoretical analysis of neuronal variability, Biophys. J. 5 (1965), pp. 173–194]). We also prove an analogue result for sequences of multivariate random variables based on the diffusion approximation in Tamborrino, Sacerdote, and Jacobsen [Weak convergence of marked point processes generated by crossings of multivariate jump processes. Applications to neural network modeling, Phys. D 288 (2014), pp. 45–52]. The weighted means studied in this paper generalize the logarithmic means. We also investigate moderate deviations.     

Tensor logarithmic norm and its applications

Matrix logarithmic norm is an important quantity, which characterize the stability of linear dynamical systems. We propose the logarithmic norms for tensors and tensor pairs, and extend some classical results from the matrix case. Moreover, the explicit forms of several tensor logarithmic norms and semi‐norms are also derived. Employing the tensor logarithmic norms, we bound the real parts of all the eigenvalues of a complex tensor and study the stability of a class of nonlinear dynamical systems. Copyright © 2016 John Wiley & Sons, Ltd.     

Corrigendum to “Convexity and concavity constants in Lorentz and Marcinkiewicz spaces” [J. Math. Anal. Appl. 343 (2008) 337-351]

In this note we state the accurate formulas of convexity and concavity constants in Lorentz spaces, correcting the formulas from Kamińska and Parrish (2008) [2].     

二元Schur凹copula的次对角部分

任意给定一个二元Schur 凹copula, 结合其自身和次对角部分, 利用取大和取小运算, 构造了一类新copula, 使得次对角部分相互重合, 讨论了新copula 的Schur 凹性与Schur 几何凹性.     

Logarithmic Estimates for the Density of Hypoelliptic Two-Parameter Diffusions

We consider a hypoelliptic two-parameter diffusion. We first prove a sharp upper bound in small time (s, t)[0, 1]² for the L^p-moments of the inverse of the Malliavin matrix of the diffusion process. Second, we establish the behaviour of2² log p_s, t(x, y), as ↓0, where x is the initial condition of the diffusion, = , and p_s, t(x, y) is the density of the hypoelliptic two-parameter diffusion.