The restricted EM algorithm under linear inequalities in a linear model with missing data

This paper discusses the maximum likelihood estimate of βunder linear inequalities A0β≥a in a linear model with missing data, proposes the restricted EM algorithm and proves the convergence.     

独立Poisson分布的均值之MLE的改进

In this paper, we consider the simultaneous estimation of the parameters (means) of the independent Poisson distribution by using the following loss functions: L0(θ,T)=∑i=1^n(Ti-θi)^2,L1(θ,T)=∑i=1^n(Ti-θi)^2/θi We develop an estimator which is better than the maximum likelihood estimator X simultaneously under L0(θ, T) and L1(θ, T). Our estimator possesses substantially smaller risk than the usual estimator X to estimate the parameters (means) of the independent Poisson distribution.     

Existence of unbiased estimate of regression parameters in simple linear EV models

It is well known that for one-dimensional normal EV regression model X = x u,Y =α βx e, where x, u, e are mutually independent normal variables and Eu=Ee=0, the regression parameters a and βare not identifiable without some restriction imposed on the parameters. This paper discusses the problem of existence of unbiased estimate for a and βunder some restrictions commonly used in practice. It is proved that the unbiased estimate does not exist under many such restrictions. We also point out one important case in which the unbiased estimates of a and βexist, and the form of the MVUE of a and βare also given.     

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.     

Jackknife empirical likelihood test for the equality of degrees of freedom in t-copulas

It has been argued that fitting a t-copula to financial data is superior to a normal copula. To overcome the shortcoming that a t-copula only has one parameter for the degrees of freedom, the t-copula with multiple parameters of degrees of freedom has been proposed in the literature, which generalizes both the t-copulas and the grouped t-copulas. Like the inference for a t-copula, a computationally efficient inference procedure is to first estimate the correlation matrix via Kendall's τ and then to estimate the parameters of degrees of freedom via pseudo maximum likelihood estimation. This paper proposes a jackknife empirical likelihood test for testing the equality of some parameters of degrees of freedom based on this two-step inference procedure, and shows that the Wilks theorem holds.     

序约束下AR(p)-ARCH(q)模型参数的估计与检验

In this paper, we study a stationary AR(p)-ARCH(q) model with parameter vectors a and β. We propose a method for computing the maximum likelihood estimator (MLE) of parameters under the nonnegative restriction. A similar method is also proposed for the case that the parameters are restricted by a simple order: α1≥α2≥…≥αq, andβ1≥β2≥…βp. The strong consistency of the above two estimators is discussed. Furthermore, we consider the problem of testing homogeneity of parameters against the simple order restriction. We give the likelihood ratio (LR) test statistic for the testing problem and derive its asymptotic null distribution.     

Comparison of two variances under inequality constraints by using empirical likelihood method

In this article, the empirical likelihood introduced by Owen Biometrika, 75, 237-249 （1988） is applied to test the variances of two populations under inequality constraints on the parameter space. One reason that we do the research is because many literatures in this area are limited to testing the mean of one population or means of more than one populations; the other but much more important reason is： even if two or more populations are considered, the parameter space is always without constraint. In reality, parameter space with some kind of constraints can be met everywhere. Nuisance parameter is unavoidable in this case and makes the estimators unstable. Therefore the analysis on it becomes rather complicated. We focus our work on the relatively complicated testing issue over two variances under inequality constraints, leaving the issue over two means to be its simple ratiocination. We prove that the limiting distribution of the empirical likelihood ratio test statistic is either a single chi-square distribution or the mixture of two equally weighted chi-square distributions.     

Empirical likelihood estimation of discretely sampled processes of OU type

This paper presents an empirical likelihood estimation procedure for parameters of the discretely sampled process of Ornstein-Uhlenbeck type. The proposed procedure is based on the condi- tional characteristic function, and the maximum empirical likelihood estimator is proved to be consistent and asymptotically normal. Moreover, this estimator is shown to be asymptotically efficient under some mild conditions. When the background driving Lévy process is of type A or B, we show that the intensity parameter c...     

Modified likelihood ratio test for homogeneity in normal mixtures with two samples

This paper investigates the modified likelihood ratio test（LRT） for homogeneity in normal mixtures of two samples with mixing proportions unknown. It is proved that the limit distribution of the modified likelihood ratio test is X^2（1）.     

鞅差误差下非参数模型的小波估计

This paper is concerned with the heteroscedastic regression model Y1=g(xi) σiei, (1≤i≤n) under correlated errors ei,where it is assumed that σi^2 =f(ui),the design points (xi,u1)are known and nonrandom, and g and f are unknown functions. Assuming that unobserved disturbances ei are martingale differences. The strong uniform convergence rates and r-th moment uniform convergence rates of wavelet estimator of g are investigated. Also,the strong uniform convergence rates are discussed for wavelet estimator of f.     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

Journal of the Operations Research Society of China Special issue on Operations Research in Healthcare Management

正Guest Editors:Hong Chen,Shanghai Jiao Tong University,Shanghai,China Guohua Wan,Shanghai Jiao Tong University,Shanghai,China David Yao,Columbia University,New York,USA Scope:Healthcare delivery worldwide has been fraught with high cost,low efficiency and poor quality of patient care service.For the field of operations research(OR),healthcare offers some of the biggest challenges as well as best opportunities in     

ANALYSIS IN THEORY AND APPLICATIONS Vol. 30, 2014 CONTENTS

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An alternative mathematical algorithm for the photo- and videokeratoscope

Due to the resolution of current laser technology, the accuracy of corneal topography as measured by the videokeratoscope is no longer adequate to provide precise enough data for refractive surgery or for the fitting of customized contact lenses. We present an algorithm for recovering corneal topography that makes use of modern differential geometric techniques and numerical descent in Sobolev spaces. We believe this algorithm may be used with the photo- and videokeratoscope to increase the accuracy of the recovered corneal topography.     

A note on Sobolev orthogonality for Laguerre matrix polynomials

Let {Ln(A,λ)(x)}n≥0 be the sequence of monic Laguerre matrix polynomials defined on [0, ∞) by Ln(A,λ)(x)=n!/(-λ)n∑nk=0(-λ)κ/k!(n-1)! (A I)n[(A I)k]-1 xk,where A ∈ Cr×r. It is known that {Ln(A,λ)(x)}n≥0 is orthogonal with respect to a matrix moment functional when A satisfies the spectral condition that Re(z) ＞ - 1 for every z ∈σ(A).In this note we show that forA such that σ(A) does not contain negative integers, the Laguerre matrix polynomials Ln(A,λ) (x) are orthogonal with respect to a non-diagonal SobolevLaguerre matrix moment functional, which extends two cases: the above matrix case and the known scalar case.     

CONTENTS OF VOLUME 30

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