Error bounds for asymptotic expansions of the distribution of the MLE in a GMANOVA model

Summary In this paper we obtain asymptotic expansions for the distribution function and the density function of a linear combination of the MLE in a GMANOVA model, and for the density function of the MLE itself. We also obtain certain error bounds for the asymptotic expansions.     

The distribution of a generalized least squares estimator with covariance adjustment

The distribution theory is developed for a generalized least squares estimator of the growth curve model. A special case of the estimator is the maximum likelihood estimator which is weighted by the sample covariance matrix. The distribution of two conditional forms of the estimator are derived and from these its density is obtained. Two general pivots and their distributions are derived from the conditional forms and special cases of these are investigated. The results obtained are linked to carlier work.     

General Regular Variation of n-th Order and the 2nd Order Edgeworth Expansion of the Extreme Value Distribution （Ⅰ）

In Part Ⅰ the concept of the general regular variation of n-th order is proposed and its construction is discussed. The uniqueness of the standard expression and the higher order regularity of the auxiliary functions are proved.     

On the normality a posteriori for exponential distributions,using the Bayesian estimation

Summary The Bayesian estimation problem for the parameter θ of an exponential probability distribution is considered, when it is assumed that θ has a natural conjugate prior density and a loss-function depending on the squared error is used. It is shown that, with probability one, the posterior density of the Bayesian—centered and scaled parameter converges pointwise to the normal probability density. The weak convergence of the posterior distributions to the normal distribution follows directly. Both correct and incorrect models are studied and the asymptotic normality is stated respectively.     

Characterization of a Marshall-Olkin type class of distributions

Summary A class of bivariate distributions that generalize Marshall-Olkin's one is characterized through a functional equation which involves two associative operations. The obtained distributions concentrate positive mass on the linex=y when the two associative operations coincide; otherwise a positive mass is concentrated on a continuous monotone function. Work performed while the authors were members of CNR-GNAFA.     

胰岛素分子主链构象的CNDO／2计算和比较

对蛋白质分子进行量子化学计算常采用如下方法:以肽基和残基侧链为基本计算单元,使对蛋白质分子的计算分解成各次单元的计算(图10)。计算时往往根据构象图选择代表点以减少工作量。例如,计算木瓜蛋白酶时,根据其构象图,212个肽基被分为10组,每组中选取1个代表点进行计算。用同样的方法处理残基侧链的计算。但该方法     

Large-deviation probabilities for maxima of sums of subexponential random variables with application to finite-time ruin probabilities

We establish an asymptotic relation for the large-deviation probabilities of the maxima of sums of subexponential random variables centered by multiples of order statistics of i.i.d.standard uniform random variables.This extends a corresponding result of Korshunov.As an application,we generalize a result of Tang,the uniform asymptotic estimate for the finite-time ruin probability,to the whole strongly subexponential class.     

Synthesis of PMMA‐b‐PBA block copolymer in homogeneous and miniemulsion systems by DPE controlled radical polymerization

In this research, poly(methyl methacrylate)‐b‐poly(butyl acrylate) (PMMA‐b‐PBA) block copolymers were prepared by 1,1‐diphenylethene (DPE) controlled radical polymerization in homogeneous and miniemulsion systems. First, monomer methyl methacrylate (MMA), initiator 2,2′‐azobisisobutyronitrile (AIBN) and a control agent DPE were bulk polymerized to form the DPE‐containing PMMA macroinitiator. Then the DPE‐containing PMMA was heated in the presence of a second monomer BA, the block copolymer was synthesized successfully. The effects of solvent and polymerization methods (homogeneous polymerization or miniemulsion polymerization) on the reaction rate, controlled living character, molecular weight (M_n) and molecular weight distribution (PDI) of polymers throughout the polymerization were studied and discussed. The results showed that, increasing the amounts of solvent reduced the reaction rate and viscosity of the polymerization system. It allowed more activation–deactivation cycles to occur at a given conversion thus better controlled living character and narrower molecular weight distribution of polymers were demonstrated throughout the polymerization. Furthermore, the polymerization carried out in miniemulsion system exhibited higher reaction rate and better controlled living character than those in homogeneous system. It was attributed to the compartmentalization of growing radicals and the enhanced deactivation reaction of DPE controlled radical polymerization in miniemulsified droplets. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 4435–4445, 2009     

Tail Dependence Comparison of Survival Marshall–Olkin Copulas

The multivariate tail dependence describes the amount of dependence in the upper-orthant tail or lower-orthant tail of a multivariate distribution and can be used in the study of dependence among extreme values. We derive an explicit expression of tail dependence of multivariate survival Marshall–Olkin copulas, and obtain a sufficient condition under which tail dependencies of two survival Marshall–Olkin copulas can be compared. Some examples are also presented to illustrate our results.      

The effect of Co(II)‐mediated catalytic chain transfer on the emulsion polymerization kinetics of methyl methacrylate

The effect the catalytic chain transfer agent, bis[(difluoroboryl) dimethylglyoximato] cobalt(II) (COBF), on the course of the ab initio emulsion polymerization of methyl methacrylate, and the product properties in terms of the molecular weight distribution were investigated. The emulsion polymerization kinetics have been studied with varying surfactant, initiator, and COBF concentrations. The experimentally determined average number of radicals per particle strongly depends on the concentration of COBF and proves to be in good agreement with the results of model calculations. The apparent chain transfer constant, determined up to high conversion, is in excellent agreement with the predicted value based on a mathematical model based on COBF partitioning and the Mayo equation. The results of this work enhance the fundamental understanding of the influence a catalytic chain transfer agent has on the course of the emulsion polymerization and the control of the molecular weight distribution. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 5078–5089, 2009