The Generalized Pascal Triangle and the Matrix Variate Jensen-Logistic Distribution

This article defines the so called Generalized Matrix Variate Jensen-Logistic distribution. The relevant applications of this class of distributions in Configuration Shape Theory consist of a more efficient computation, supported by the corresponding inference. This demands the solution of two important problems: (1) the development of analytical and efficient formulae for their k-th derivatives and (2) the use of the derivatives to transform the configuration density into a polynomial density under some special matrix Kummer relation, indexed in this case by the Jensen-Logistic kernel. In this article, we solve these problems by deriving a simple formula for the k-th derivative of the density function, avoiding the usual partition theory framework and using a generalization of Pascal triangles. Then we apply the results by obtaining the associated Jensen-Logistic Kummer relations and the configuration polynomial density in the setting of Statistical Shape Theory.     

Exact power comparison of three criteria to assess the independence between two sets of variates

Powers of the three criteria are evaluated for testing the hypothesis of the independence between a -set and a q-set of variates in a (p + q) -variate normal population. They are: (1) the likelihood ratio type criterion, Wt (2) the largest root criterion, r1, and (3) criterion of the sum of roots, V. For p= 2, Pillai and Jayachandran, and others have studied for the restricted range of the alternative hypothesis. Recently the power of the largest root was investigated in detail by Sugiyama and %%. In this paper, their power functions are compared in a wide range of the alternative hypotheses. The powers of rl and V are locally optimum, but the W shows a large power in a wide range.     

Zonal Polynomials and Hypergeometric Functions of Quaternion Matrix Argument

We define zonal polynomials of quaternion matrix argument and deduce some impor-tant formulae of zonal polynomials and hypergeometric functions of quaternion matrix argument. As an application, we give the distributions of the largest and smallest eigenvalues of a quaternion central Wishart matrix W ～ ?W(n, Σ), respectively.     

Estimation of a linear transformation and an associated distributional problem

A multivariate “errors in variables” regression model is proposed which generalizes a model previously considered by Gleser and Watson (1973). Maximum likelihood estimators [MLE's] for the parameters of this model are obtained, and the consistency properties of these estimators are investigated. Distribution of the MLE of the “error” variance is obtained in a simple case while the mean and the variance of the estimator are obtained in this case without appealing to the exact distribution.     

Asymptotic linearity and limit distributions,approximations

Linear and quadratic forms as well as other low degree polynomials play an important role in statistical inference. Asymptotic results and limit distributions are obtained for a class of statistics depending on μ+X$\mu +\mathbf{X}$, with X any random vector and μ$\mu$ non-random vector with ∥μ∥→+∞$\parallel \mu \parallel \to +\infty$. This class contain the polynomials in μ+X$\mu +\mathbf{X}$. An application to the case of normal X is presented. This application includes a new central limit theorem which is connected with the increase of non-centrality for samples of fixed size. Moreover upper bounds for the suprema of the differences between exact and approximate distributions and their quantiles are obtained.     

Stochastic modeling of particle movement with application to marine biology and oceanography

We consider some stochastic models that have been proposed for the trajectories of moving objects, including Brownian motion. This leads to the development of a general approach for dealing with paths including the use of functional stochastic differential equations. We then present an empirical example based on the surface drifting movements of a small satellite-linked radio transmitter tag after it detached from a whale shark in the western Indian Ocean. The daily estimates of the tag’s locations were determined from transmissions received at irregular times by polar-orbiting satellites of the Argos Data Collection and Location Service system.     

微分多项式的零点

设f（z）是超越亚纯函数,ψ是关于f的微分多项式,满足条件;本文得出了ψ零点的几个结果,改进并推广了C．C．Yang、仪洪勋等人的有关定理。     

亚纯函数多项式的导数

设f（z）是平面上的亚纯函数，P[f]是f的n次常系数多项式，Q[f]是f的微分多项式，满足（r,f）＋（r,）=S（r，f），其中vQ≤n－2，本文考虑P'[f]＋Q的值分布，推广了W.K.Hayman，J.Clunie，E.Mues等人关于整函数的结果，并进一步改进了文[3]的结果。     

Inference in affine shape theory under elliptical models

This paper studies the elliptical statistical affine shape theory under certain particular conditions on the evenness or oddness of the number of landmarks. In such a case, the related distributions are polynomials, and the inference is easily performed; as an example, a landmark data is studied, and the performance of the polynomial density versus the usual series density is compared.     

Bimatrix variate gamma-beta distributions

Two bimatrix distributions with beta and gamma marginals are introduced. Various properties (including product moments of determinants and traces, entropies, marginal distributions) are derived. Parameter estimation by the method of maximum likelihood is discussed. The performance and efficiencies of the maximum likelihood estimators and the associated confidence intervals are assessed by simulation. The efficiencies are compared versus those for the maximum likelihood estimators and the associated confidence intervals based on matrix variate gamma distributions. A discussion of possible applications of the bimatrix distributions is given.