约束极小极大问题的光滑化牛顿方法

对极小极大问题在K-T条件下的解决方法进行了研究，用光滑化方法将不可微非线性方程组转化为可微非线性方程组，并用牛顿法来求解这个方程组，最后给出了3个算例来验证此方法。     

胎次递进人口方程组解的一个性质

本文利用泛函分析的方法证明了下述结果:胎次递进人口方程组的解在某种意义下连续地依赖于胎次递进比{λ_0(s),λ_1(s),…λ_N(s)},本结果具有实际意义.     

线性方程组的单调收敛

本文讨论了线性方程组Au=b的单调收敛性,给出了某些线性方程组Au=b占之单调收敛性的判定条件.     

Estimation of regression parameters in generalized linear models for cluster correlated data with measurement error

Liang and Zeger (1986) introduced a class of estimating equations that gives consistent estimates of regression parameters and of their asymptotic variances in the class of generalized linear models for cluster correlated data. When the independent variables or covariates in such models are subject to measurement errors, the parameter estimates obtained from these estimating equations are no longer consistent. To correct for the effect of measurement errors, an estimator with smaller asymptotic bias is constructed along the lines of Stefanski (1985), assuming that the measurement error variance is either known or estimable. The asymptotic distribution of the bias-corrected estimator and a consistent estimator of its asymptotic variance are also given. The special case of a binary logistic regression model is studied in detail. For this case, methods based on conditional scores and quasilikelihood are also extended to cluster correlated data. Results of a small simulation study on the performance of the proposed estimators and associated tests of hypotheses are reported.     

Sieve Empirical Likelihood and Extensions of the Generalized Least Squares

The empirical likelihood cannot be used directly sometimes when an infinite dimensional parameter of interest is involved. To overcome this difficulty, the sieve empirical likelihoods are introduced in this paper. Based on the sieve empirical likelihoods, a unified procedure is developed for estimation of constrained parametric or non-parametric regression models with unspecified error distributions. It shows some interesting connections with certain extensions of the generalized least squares approach. A general asymptotic theory is provided. In the parametric regression setting it is shown that under certain regularity conditions the proposed estimators are asymptotically efficient even if the restriction functions are discontinuous. In the non-parametric regression setting the convergence rate of the maximum estimator based on the sieve empirical likelihood is given. In both settings, it is shown that the estimator is adaptive for the inhomogeneity of conditional error distributions with respect to predictor, especially for heteroscedasticity.     

Banach空间二阶微分方程两点边值问题的解

本文利用单调迭代法，研究了Ｂａｎａｃｈ空间二阶微分方程两点边值问题解的存在唯一性并改进和推广了一些新近结果。     

用偏导数法求解一类二元函数方程

给出了形如f（w（xy））=R（f（x）f（y））的二元函数方程可微解的偏导数求法，将此类二元函数方程的求解归结为一阶常微分方程的求解问题     

Broer-Kaup方程组的新类孤子解

本文通过适当变换,将Broer-Kaup方程组变为一个简单的方程,然后利用比较广泛的假设,用Riccati方程的解来构造该方程的解,得到了Broer-Kaup方程组的新类孤子解。     

An estimating equation for parametric shared frailty models with marginal additive hazards

Summary.  Multivariate failure time data arise when data consist of clusters in which the failure times may be dependent. A popular approach to such data is the marginal proportional hazards model with estimation under the working independence assumption. In some contexts, however, it may be more reasonable to use the marginal additive hazards model. We derive asymptotic properties of the Lin and Ying estimators for the marginal additive hazards model for multivariate failure time data. Furthermore we suggest estimating equations for the regression parameters and association parameters in parametric shared frailty models with marginal additive hazards by using the Lin and Ying estimators. We give the large sample properties of the estimators arising from these estimating equations and investigate their small sample properties by Monte Carlo simulation. A real example is provided for illustration.     

Body Mass Index, Perceived Health, and Happiness: Their Determinants and Structural Relationships

The structural relationships between body mass index, perceived health and happiness have been studied in a survey of 700 native Dutch citizens. We found an indirect effect of body mass index on happiness, via perceived health. Age had an inverted U-shaped relationship with body mass index, and both education and smoking had a negative effect on body mass index. Being married, doing paid work, owning a house, and doing sports had positive effects on perceived health, suggesting that living a regular life may lead to a better perceived health. Being married positively affected happiness. The other socio-demographic variables either had no effects on happiness or indirect effects via body mass index and perceived health.