非平衡随机效应模型中方差分量的经验Bayes估计

对非平衡单向分类随机效应模型中方差分量找到了其最小充分统计量,在加权平方损失下导出了其Bayes估计,利用多元密度及其偏导数的核估计方法构造了方差分量的经验Bayes(EB)估计,并导出了其收敛速度.文末用例子说明了符合定理条件的先验分布是存在的.     

A new estimate of the parameters in linear mixed models

In linear mixed models, there are two kinds of unknown parameters: one is the fixed effect, the other is the variance component. In this paper, new estimates of these parameters, called the spectral decomposition estimates, are proposed, Some important statistical properties of the new estimates are established, in particular the linearity of the estimates of the fixed effects with many statistical optimalities. A new method is applied to two important models which are used in economics, finance, and mechanical fields. All estimates obtained have good statistical and practical meaning.     

The term structure of interest rates in the economic and monetary union

The main purpose of this article is to present a new numerical procedure that can be used to implement a variety of different interest rate models. The new approach allows to construct no-arbitrage models for the term structure, where the stochastic process driving the rates is infinitely divisible, as in the cases of pure-diffusion and jump-diffusion mean reverting models. The new method determines a unique fully specified hexanomial tree, consistent with risk neutral probabilities. A simple forward recursive procedure solves for the entire tree. The proposed lattice model, which generalized the Hull and White [37] single-factor model, is relatively simple, computational efficient and can fit any initial term structure observed in the market. Numerical experiments demonstrate how the jump-diffusion mean reverting model is particularly suited to describe the European money market rates behavior. Interest rates controlled by the monetary authorities behave as if they are jump processes and the term structure, at short maturity, is contingent upon the levels of these official rates.     

A Classification of Reproducible Natural Exponential Families in the Broad Sense

Let be a positive Radon measure on having a Laplace transform L and F=F() be a natural exponential family (NEF) generated by . A positive Radon measure with >0 and its associated NEF F =F( ) are called the th convolution powers of and F, respectively, if . Let f _, (F) be the image of an NEF F under the affine transformation f _, :xx+. If for a given NEF F, there exists a triple (,,) in such that f _, (F)=F , we call F a reproducible NEF in the broad sense. In other words, an NEF F is reproducible in the broad sense if a convolution power of F equals an affine transformation of F. Clearly, for =1, F is reproducible in the broad sense if there exists an affinity under which F is invariant. In this paper we obtain a complete classification of the class of reproducible NEF's in the broad sense. We show that this class is composed of infinitely divisible NEF's and that it contains the class of NEF's having exponential and power variance functions as well as NEF's constituting discrete versions of the latter NEF's. We also provide a characterization of the reproducible NEF's in the broad sense in terms of their associated exponential dispersion models.     

How the design of an experiment influences the nonsensitiveness regions in models with variance components

Nonsensitiveness regions for estimators of linear functions, for confidence ellipsoids, for the level of a test of a linear hypothesis on parameters and for the value of the power function are investigated in a linear model with variance components.The influence of the design of an experiment on the nonsensitiveness regions mentioned is numerically demonstrated and discussed on an example.     

Reliability and non-reliability studies of Poisson variables in series and parallel systems

In this paper, we have derived the distribution of the minimum and maximum of two independent Poisson random variables. A useful procedure for computing the probabilities is given and a total of four numerical examples are presented. Of these four examples, the first two are on the generated data and the other two are on the Champion League Soccer data in order to illustrate the model which is considered here. The hazard rate and the reversed hazard rate, of the minimum and maximum of two independent discrete random variables, are also obtained and their monotonicity is investigated. The results for the Poisson-distributed variables are obtained as special cases.     

Convergence rates and interior estimates in homogenization of higher order elliptic systems

This paper is concerned with the quantitative homogenization of 2m-order elliptic systems with bounded measurable, rapidly oscillating periodic coefficients. We establish the sharp $O(\epsilon )$ convergence rate in $W^{m?1,p_0}$ with $p_0=\frac{2d}{d?1}$ in a bounded Lipschitz domain in ${\mathbb{R}}^d$ as well as the uniform large-scale interior $C^{m?1,1}$ estimate. With additional smoothness assumptions, the uniform interior $C^{m?1,1}$, $W^{m,p}$ and $C^{m?1,\alpha }$ estimates are also obtained. As applications of the regularity estimates, we establish asymptotic expansions for fundamental solutions.     

Simultaneous optimal estimates of fixed effects and variance components in the mixed model

For a general linear mixed model with two variance components, a set of simple conditions is obtained, under which, (i) the least squares estimate of the fixed effects and the analysis of variance (ANOVA) estimates of variance components are proved to be uniformly minimum variance unbiased estimates simultaneously; (ii) the exact confidence intervals of the fixed effects and uniformly optimal unbiased tests on variance components are given; (iii) the exact probability expression of ANOVA estimates of variance components taking negative value is obtained.     

Convergence Rate of the L-N Estimator in Poisson-Gamma Models

We focus on in this paper the convergence rate of the L-N estimators for the fixed effect β in Poisson-Gamma models which are typical hierarchical generalised linear models（HGLMs）. Under the proper assumptions on response variables and some smoothing conditions, we obtain the strong consistency and the convergence rate of the L-N estimator based on the combination of L-N and quasi-likelihood.     

Convergence rates in the central limit theorem for stationary mixing sequences of random vectors

Uniform and nonuniform Berry-Esseen bounds are given for strongly mixing and uniformly mixing stationary sequences of random vectors. The proofs are based on the classical Bernstein procedure.     

On structuring problems of job design met in the development and maintenance of information systems

In the development and maintenance of information systems data processing tasks are assigned either to a computer or to a man. In this paper we consider five decisions made during the development phase. These decisions have an influence on the contents of jobs: 1. distribution of work between man and computer, 2. construction of man-computer interface, 3. grouping tasks into jobs, 4. design of control part of new information system, 5. assignment of people to jobs.During the use of an information system both the person and his job will change. Here various combinations of changes in a person-job pair are classified and analyzed.This research has been supported by the Academy of Finland.     

沪深股指波动的杠杆效应和星期效应分析

在TGARCH模型中引入哑变量以同时反映条件方差波动的不对称性和星期特征,并运用其对沪深股指波动特征进行了实证分析.结果表明沪深股指波动存在着明显的杠杆效应和星期效应.     

Joint modelling of location and scale parameters of the skew-normal distribution

Joint location and scale models of the skew-normal distribution provide useful ex- tension for joint mean and variance models of the normal distribution when the data set under consideration involves asymmetric outcomes. This paper focuses on the maximum likelihood estimation of joint location and scale models of the skew-normal distribution. The proposed procedure can simultaneously estimate parameters in the location model and the scale model. Simulation studies and a real example are used to illustrate the proposed methodologies.     

Fitting sampling distribution agreeing in support and moments and tables of critical values of sphericity criterion

Mixtures of two beta or gamma distributions having given first four, three, or two moments are found and applied to tabulate to three decimals critical values of the locally most powerful criterion of sphericity or proportions of moments of order two of a p-variate normal distribution. Expressions are given for the first four moments of the test statistic.     

Globally stable vaccine-induced eradication of horizontally and vertically transmitted infectious diseases with periodic contact rates and disease-dependent demographic factors in the population

Within the framework of SEIR-like epidemic models, we studied the conditions for the stable eradication of some families of vertically and horizontally transmitted infectious diseases in the case of periodically varying contact rate. By means of Floquet’s theory, we found a condition for the eradication solution to be locally asymptotically stable. We then demonstrated that the same condition guarantees also that this vaccine-induced disease-free solution is globally asymptotically stable. A model with interacting populations is also considered. In the final part of this work, we extended the model by taking into account the variation of population size, the impact of disease-related deaths and reduction of fertility.     

Adaptive stabilization and regulator design for distributed-parameter systems in the case of collocated actuators and sensors

In this paper, we consider adaptive stabilization and an adaptiveregulator design for collocated distributed-parameter systemsin the case of the input and output operators being unbounded.Adaptive stabilization is realized by the concept of high-gainoutput feedback. The adaptive regulator is constructed via theconcept of high-gain output feedback, using a mechanism to estimatethe unknown parameters of the bounded disturbances. The stateof the controlled system is shown to converge to zero.     

A local limit theorem for the number of nodes,the height,and the number of final leaves in a critical branching process tree

Let Z_i be the number of particles in the ith generation of a non-degenerate critical Bienaymé-Galton-Watson process with offspring distribution $ p_r = P \{\hbox{a given individual has {\it r} children}\},\kern2em r\geq 0. $ Let ν = Σ^infinity₀ Z_j be the total progeny and let ζ = inf{r: Z_r = 0} be the extinction time. Equivalently, ν and ζ are the total number of nodes and (1 + the height), respectively, of the family tree of the branching process. Assume that E{Z₁} = Σ p_rr = 1 and E{Z₁^{3 + δ}} = Σ p_rr^{3 + δ} < infinity for some δ ϵ (0, 1). We find an asymptotic formula with remainder term for k⁴P{ζ = k + 1, Z_k = ℓ ν = n} when k→ infinity, which is uniform over n and ℓ. This is used to confirm a conjecture by Wilf that the number of leaves in the last generation of a randomly chosen rooted tree converges in distribution. More precisely, in the terminology introduced above, there exists a probability distribution {q₁} such that for n → infinity $ P\{Z_{\zeta-1} = l | \nu=n\} = q_l + O \left({{\log^3 n } \over {n^{1/2}}}\right), $ uniformly over ℓ ≥1. The limiting distribution is identified by means of a functional equation for the generating function Σ^infinity₁ q s^ℓ. Numerically, q₁ ≅ 0.0602, q₂ ≅ 0.248, q₃ ≅ 0.094, and q₄ ≅ 0.035. Our method can also be used to find lim _{k→ infinity} k⁴P{ζ = k + 1, Z_k = ℓ ν = n} when only E{Z₁^{2 + δ}} < infinity for some 0 ≤δ≤1, but we do not treat this case here; it goes without saying that the fewer moment assumptions one makes, the poorer the estimates become. © 1996 John Wiley & Sons, Inc.     

Conditioned rates of convergence in the CLT for sums and maximum sums

An interesting recent result of Landers and Roggé (1977, Ann. Probability5, 595–600) is investigated further. Rates of convergence in the conditioned central limit theorem are developed for partial sums and maximum partial sums, with positive mean and zero mean separately, of sequences of independent identically distributed random variables. As corollaries we obtain a conditioned central limit theorem for maximum partial sums both for positive and zero mean cases.     

Analysis of an MMPP/G/1/K queue with queue length dependent arrival rates,and its application to preventive congestion control in telecommunication networks

Recently telecommunication networks have been designed in order to transfer all types of information services such as voice, data and video. Next generation wireless networks has been developed to integrate the existing technologies and to support comprehensive services. As the traffics of diverse services have properties of timecorrelation and burstiness, unpredictable statistical fluctuation of traffic streams may cause congestion. To suggest a congestion control scheme which controls arrival rates according to the queue length, we consider an MMPP/G/1/K queue with queue length dependent arrival rates. The effect of system parameters on performance measures also is explained with the numerical examples.