随机设计非线性混合模型的统计分析

本文研究了个体观察次数为随机的非线性 混合效应模型中参数的点估计以及区间估计. 在仅给出适当的矩条件下, 给出了固定效应、随机效应的方差阵以及误差方差的矩估计, 并证明了估计量的相合性及渐近正态性. 为给出误差方差以及随机效应方差分量的置信区间, 本文也给出了误差及随机效应的四阶矩估计. 随机模拟说明了方法的有效性.     

Competitive exclusion and coexistence in a Leslie–Gower competition model with Allee effects

The classical competitive exclusion principle states that two populations competing for a limited resource cannot coexist, one of the populations will drive the other to extinction. We prove in this work that when one population is subject to Allee effects, then for certain parameter regimes both competing populations may either coexist or one population may drive the other to extinction depending on initial conditions.     

Multiple attractors in a Leslie–Gower competition system with Allee effects

We investigate asymptotic dynamics of the classical Leslie–Gower competition model when both competing populations are subject to Allee effects. The system may possess four interior steady states. It is proved that for certain parameter regimes both competing populations may either go extinct, coexist or one population drives the other population to extinction depending on initial conditions.     

Case Influence Analysis in Bayesian Inference

Abstract

We demonstrate how case influence analysis, commonly used in regression, can be applied to Bayesian hierarchical models. Draws from the joint posterior distribution of parameters are importance weighted to reflect the effect of deleting each observation in turn; the ensuing changes in the posterior distribution of each parameter are displayed graphically. The procedure is particularly useful when drawing a sample from the posterior distribution requires extensive calculations (as with a Markov Chain Monte Carlo sampler). The structure of hierarchical models, and other models with local dependence, makes the importance weights inexpensive to calculate with little additional programming. Some new alternative weighting schemes are described that extend the range of problems in which reweighting can be used to assess influence. Applications to a growth curve model and a complex hierarchical model for opinion data are described. Our focus on case influence on parameters is complementary to other work that measures influence by distances between posterior or predictive distributions.     

连续时间下局部光滑统计量的a.s.收敛速度和边界效应

本文在连续时间场合研究回归函数的非参数估计量之一———局部光滑统计量的性质 .不仅给出其a.s.收敛的一个速度 ,而且证明了该统计量不受边界效应影响的优良性质 ;同时指出了在连续时间的场合 ,估计量中窗宽的选择和样本的轨道性质都对该估计量的性质产生重要的影响     

Diffraction of sound waves by a rigid cylindrical cavity of finite length with an internal impedance surface

A rigorous solution is presented for the problem of diffraction of plane harmonic sound waves by a cavity formed by a terminated rigid cylindrical waveguide of finite length whose interior surface is lined by an acoustically absorbent material. The solution is obtained by a modification of the Wiener-Hopf technique and involve an infinite series of unknowns, which are determined from an infinite system of linear algebraic equations. Numerical solution of this system is obtained for various values of the parameters of the problem and their effects on the diffraction phenomenon are shown graphically.Received: December 12, 2001     

Exact solution of thermal radiation on MHD flow over a stretching porous sheet

The effect of radiation on MHD steady asymmetric flow of an electrically conducting fluid past a stretching porous sheet in the presence of radiation has been analyzed. Exact solutions for the velocity and temperature fields have been derived and the effects of radiation, magnetic, Prandtl number, wall temperature and suction (or injection) parameters have been studied with the help of graphs.     

regularizing effect in a nonlinear, degenerate parabolic equation in one space dimension

In this paper we provide and analyze a nonlinear degenerate parabolic equation in one space dimension with the following smoothing property: If the initial data is only uniformly continuous, at positive times, the solution has bounded second derivatives (it belongs to ). We call this surprising phenomenon a regularizing effect. So far, such phenomena have only been observed in uniformly parabolic equations.

     

非线性纵向数据模型中自相关性和随机效应的存在性检验

刻画纵向数据协方差结构有三种可能因素 ,即序列相关 (特别是一阶自相关 )、随机效应和常规的随机误差 (Diggleetal,2 0 0 2 ) .本文研究非线性纵向数据模型的自相关性和随机效应存在性的单个和联合检验 ,得到了检验的score统计量 ,并利用血浆药物渗透数据 (Davidian&Gilinan ,1 995)说明检验方法的应用 .     

Field Theory Approach to the Dynamics of a Continuous Medium: A Perturbation Theory

We propose a perturbation theory that allows solving the equations of motion for the displacement vector in the body of the Earth in the framework of the linear theory of elasticity. We show that tectonic processes are primarily determined by tidal actions. We analyze the tidal effects in the Earth–Moon–Sun system.