Some applications,properties and conjectures for higher order cumulants of a markovian stepping-stone model

This paper investigates certain tridiagonal coefficient matrices from linear differential equations for the joint cumulants of a Markovian stepping-stone model. The model is used to describe the dynamics of insect population growth, and is illustrated with an application to the spread of Africanized honey bees. The coefficient matrices are shown to have certain structure. A conjecture concerning their eigenvalues is proven for a special case of interest, and is also investigated numerically and by symbolic mathematical analysis.     

On two asymptotic normal distributions for the generalized wilks lambda statistic

In this paper we.present a Normal asymptotic distribution for the logarithm of the generalized Wilks Lambda statistic based on an asymptotic distribution for the determinant of a Wishart matrix. This distribution is obtained through the combined use of Taylor expansions of random variables whose exponentials have chi-square distributions and the Lindeberg-Feller version of the Central Limit Theorem, Another asymptotic Normal distribution for the logarithm of the generalized Wilks Lambda statistic for the case when at most one of the sets has an odd number of variables is derived directly from the exact distribution. Both distributions are non-degenerate and non-singular. The first Normal distribution compares favorably with other known approximations and asymptotic distributions namely for large numbers of variables and small sample sizes, while the second Normal distribution, which has a more restricted application, compares in most cases highly favorably with other known asymptotic distributions and approximations. Finally, a method to compute approximate quantiles which lay very close and converge steadily to the exact ones is presented.     

Nonnull distribution of Wilks' statistic for Manova in the complex case

In this paper, the exact distribution of Wilks' likelihood ratio criterion, A, for MANOVA, in the complex case when the alternate hypothesis is of unit rank (i.e. the linear case) has been derived and the explicit expressions for the same for p = 2 and 3 (where p is the number of variates) and general f₁ (the error degrees of freedom) and f₂ (the hypothesis degrees of freedom), are given. For an unrestricted number of variables, a general form of the density and the distribution of A in this case, is also given. It has been shown that the total integral of the series obtained by taking a few terms only, rapidly approaches the theoretical value one as more terms are taken into account, and some percentage points have also been computed.     

Proof of phenomenon B

In their paper “Some application, properties and conjectures for higher order cumulants of a Markovian stepping-stone model”, Zheng and Matis make use of a conjecture known as “Phenomenon B” regarding the eigenvalues of a tridiagonal matrix having a certain form. While the conjecture was shown to hold for particular cases, it was not proven in general. To supplement the Zheng and Matis paper, a formal proof of Phenomenon B is given here.     

Convergence of a Discrete-Time Age-Structured Population Toward a Given Steady State Through Controlled Immigration

To explore the concept of stability in an age-structured population with migration, a Markov transition matrix model is built, where age classes can be of different length, and the time step is not necessarily equal to the length of the age class. The conditions under which a vector of the model has a steady population structure are identified, as well as those under which the age structure converges to a given steady state, through a series of decisions or controls of letting immigrants in or forbidding them entry into the country. The decisions are expressed as vectors of proportions of immigrants. In the steady state, when the increment of population is proportional to its size, the age- or stage-structure remains unchanged between transitions.     

Covariance Matrix Formula for Generalized Linear Models with Unknown Dispersion

In this paper, the existence of the Uniformly Minimum Risk Equivariant (UMRE) estimator of parameters in SURE model under some quadratic losses and matrix losses is studied. The necessary and sufficient conditions for existence of the UMRE estimator of linearly estimable function vectors of regression coefficients under an affine group of transformations are obtained. It is proved that no UMRE estimator of the covariance matrix under any one of two affine groups of transformations exists.     

Small sample behavior of a robust heteroskedasticity consistent covariance matrix estimator

In heteroskedastic regression models, the least squares (OLS) covariance matrix estimator is inconsistent and inference is not reliable. To deal with inconsistency one can estimate the regression coefficients by OLS, and then implement a heteroskedasticity consistent covariance matrix (HCCM) estimator. Unfortunately the HCCM estimator is biased. The bias is reduced by implementing a robust regression, and by using the robust residuals to compute the HCCM estimator (RHCCM). A Monte-Carlo study analyzes the behavior of RHCCM and of other HCCM estimators, in the presence of systematic and random heteroskedasticity, and of outliers in the explanatory variables.     

四自由度并联微操作机器人的运动学分析

分析了2RPS 2TPS型四自由度并联微操作机器人机构的运动学特性;采用微分法推导了微位移增量矩阵的一般表达式以及输入、输出位移的雅可比矩阵;建立了微操作机器人的运动学方程、速度方程、加速度方程的显式正逆表达式,为微操作机器人的动力学与控制研究奠定了理论基础。     

中国古代的矩阵论

通过对《九章算术》中方程术的研究 ,阐述了中国最早产生的矩阵理论雏形 ,并且初步探讨了中国没有形成完整的矩阵理论的原因所在     

On the Breakdown Properties of Some Multivariate M‐Functionals*

Abstract. For probability distributions on ? ^q, a detailed study of the breakdown properties of some multivariate M‐functionals related to Tyler's [Ann. Statist. 15 (1987) 234] ‘distribution‐free’ M‐functional of scatter is given. These include a symmetrized version of Tyler's M‐functional of scatter, and the multivariate t M‐functionals of location and scatter. It is shown that for ‘smooth’ distributions, the (contamination) breakdown point of Tyler's M‐functional of scatter and of its symmetrized version are 1/q and , respectively. For the multivariate t M‐functional which arises from the maximum likelihood estimate for the parameters of an elliptical t distribution on ν ≥ 1 degrees of freedom the breakdown point at smooth distributions is 1/( q + ν). Breakdown points are also obtained for general distributions, including empirical distributions. Finally, the sources of breakdown are investigated. It turns out that breakdown can only be caused by contaminating distributions that are concentrated near low‐dimensional subspaces.