纵向数据单指标模型中参数的经验似然置信域

考虑纵向数据单指标模型,针对纵向数据组间独立的特点,提出了模型中未知参数的三种经验对数似然比统计量.在适当条件下,证明了所提出的统计量依分布收敛于x~2分布,所得结果可以构造未知参数的置信域.进一步证明了所提出的纠偏的经验对数似然比有许多优良的性质.通过模拟研究对所提方法进行了说明.     

生长曲线模型中回归系数阵的极大似然估计的精确分布

对于生长曲线模型,基于理论发展和应用效果的考虑,本文引入了Gauss型误差．在此误差下,本文研究了模型中回归系数阵的极大似然估计的精确分布,求出了此分布的密度和特征函数．     

非线性半参数EV模型的经验似然置信域

考虑非参数协变量带有测量误差的非线性半参数模型,构造了模型中未知参数的经验对数似然比统计量,在测量误差分布为普通光滑分布时,证明了所提出的统计量具有渐近χ2分布,由此结果可以用来构造未知参数的置信域.另外也构造了未知参数的最小二乘估计量,并证明了它的渐近性质.就置信域及其覆盖概率大小方面,通过模拟研究比较了经验似然方法与最小二乘法的优劣.     

非线性EV回归模型中参数的经验似然置信域

本文考虑非线性EV回归模型，构造了未知参数的经验对数似然比统计量．此外，为了克服计算困难，提出了一个基于模拟的经验对数似然比统计量．在适当条件下，证明了所提出的这两种统计量都具有渐近X^2分布，所得结果可以用来构造未知参数的置信域。     

部分线性单指标EV模型中参数的经验似然置信域

考虑部分线性单指标EV模型,利用纠偏方法构造了模型中未知参数的经验对数似然比统计量.在适当条件下,证明了所提出的统计量依分布收敛于标准x2分布,所得结果可以构造未知参数的置信域.通过模拟研究在置信域精度及其覆盖概率大小方面进行了说明.     

Panel Count Data模型参数的经验似然推断

对Panel Count Data的处理越来越受到人们的关注,Sun与Wei^([1-2])基于简单的半参数模型,提出了Panel Count Data的回归分析,并且给出了参数的估计方程。本文则基于经验似然的思想,讨论了上述Panel Count Data模型参数的置信域构造问题,特别仅通过经验似然置信区域给出了参数估计的方差阵估计,证明了估计的1/n相合性。基于Sun与Wei所给的数据,给出了参数置信区域的具体构造过程和结果。通过作图比较可以看出经验似然置信域要优于依据渐近正态性所构造的置信域。我们还依据所作出的经验似然置信域对参数估计的方差矩阵进行了估计,与用传统渐近正态性得到的矩阵较为接近。     

非线性半参数回归模型中参数的经验似然置信域

该文考虑非线性半参数回归模型,构造了模型中未知参数的经验对数似然比统计量,证明了所提出的统计量具有渐近Χ²分布,由此结果可以用来构造未知参数的置信域.另外,该文也构造了未知参数 的最小二乘估计量,并证明了它的渐近性质.仅就置信域精度及其覆盖概率大小方面,通过模拟研究比较了经验似然方法与最小二乘法的优劣.     

带有缺失数据的非线性误差模型中参数的置信域

考虑协变量有测量误差且响应变量随机缺失的非线性模型.在条件分布形式已知的情况下,通过借补方法构造了参数的经验似然,提出了基于模拟的经验似然,证明了所构造的统计量都具有渐近x~2分布,所得结果可构造未知参数的置信域.     

非线性随机效应模型的置信域

本文对非线性随机效应模型,建立了微分几何框架,推广了Bates＆Wates关于非线性模型几何结构．在吡基础上,我们导出了关于固定效应参数和子集参数的置信域的曲率表示,这些结果是BatesandWates(1980),Hamilton(1986)与Wei(1994)等的推广．     

具有Rao简单结构的多元t-模型的参数区间估计

在统计推断中,模型中未知参数的区间估计是一个重要的研究内容.本文通过构造枢轴量研究了具有Rao简单结构多元￡-模型的参数区间估计,利用条件分布技巧,得到枢轴量的分布,从而获得模型中单个未知参数的置信区域以及参数的联合置信区域.     

正态条件下带AR(1)-型方差结构GMANOVA-MANOVA模型极大似然估计的小样本特征

研究了一类带一阶自回归(AR(1))-型方差结构的广义多元方差分析-多元方差分析(GMANO VA-MANOVA)模型参数极大似然估计的小样本特征.对带AR(1)-型方差结构GMANOVA-MANOVA模型,文章在正态条件下给出了参数极大似然估计存在的一个充分必要条件,讨论了极大似然估计唯一的充分条件.在该充分条件下,文章证明了相关系数极大似然估计的精确分布只与相关系数有关,并依此给出了自相关系数简单假设H0:ρ=0v.s.H1:ρ≠0的一个不需要叠代计算估计的检验,同时模拟表明该检验为无偏检验且势函数与似然比检验势函数无太大差异.     

均匀分布参数的最短置信区间

将求均匀分布未知参数的最短置信区间转化为条件极值问题,给出了均匀分布参数的最短置信区间,推广了原有的结论.     

Exact distribution of MLE of covariance matrix in a GMANOVA-MANOVA model

For a GMANOVA-MANOVA model with normal error: Y = XB1Z1 T B2Z2 T E, E- Nq×n(0, In (?) ∑), the present paper is devoted to the study of distribution of MLE, ∑, of covariance matrix ∑. The main results obtained are stated as follows: (1) When rk(Z) -rk(Z2) ≥ q-rk(X), the exact distribution of ∑ is derived, where z = (Z1,Z2), rk(A) denotes the rank of matrix A. (2) The exact distribution of |∑| is gained. (3) It is proved that ntr{[S-1 - ∑-1XM(MTXT∑-1XM)-1MTXT∑-1]∑}has X2(q_rk(x))(n-rk(z2)) distribution, where M is the matrix whose columns are the standardized orthogonal eigenvectors corresponding to the nonzero eigenvalues of XT∑-1X.     

线性约束下异方差回归模型参数的极大似然估计

运用参数的极大似然估计法,给出在线性约束条件Hβ=C下异方差回归模型参数β和λ的极大似然估计,并讨论了估计参数的性质和模型的残差.利用得到的结论对线性约束下异方差回归模型的进一步研究和应用具有一定的理论和实际价值.     

WEIBULL分布步进应力加速寿命试验损伤失效率模型参数的近似极大似然估计和逆矩估计

Bhattacharyya和Soejoeti(1980)对步进应力加速寿命试验提出损伤失效率模型(TFR模型)．本针对TFR模型，对两参数Weibull分布，在步进应力加速试验下给出了参数的近似极大似然估计和逆矩估计，并通过Montr-Carlo模拟考察了估计的精度，比较了各估计的优劣。     

MSE's of prediction in growth curve model with covariance structures

We consider the growth curve model with covariance structures: positive-definite, uniform covariance structure and serial covariance structure. Two types of prediction problems are studied in this paper. One is called the conditional prediction problem and the other is called the extended prediction problem. For both types of prediction problems, the mean squared error for a serial covariance structure is obtained for the estimates based on the conditional expectation: the mean squared error for an unrestricted covariance structure is compared with the mean squared error for a uniform covariance structure or a serial covariance structure. These results are exemplified by two sets of real data.This research was supported in part by Grant-in-Aid for general Scientific Research, The Ministry of Education, Science and Culture under Contract Number 03640239.     

On Kirchhoff's Model of Parabolic Type

In this article, the existence of a global strong solution for all finite time is derived for the Kirchhoff's model of parabolic type. Based on exponential weight function, some new regularity results which reflect the exponential decay property are obtained for the exact solution. For the related dynamics, the existence of a global attractor is shown to hold for the problem when the non-homogeneous forcing function is either independent of time or in L^∞(L²). With the finite element Galerkin method applied in spatial direction keeping time variable continuous, a semidiscrete scheme is analyzed, and it is also established that the semidiscrete system has a global discrete attractor. Optimal error estimates in L^∞(H¹) norm are derived which are valid uniformly in time. Further, based on a backward Euler method, a completely discrete scheme is analyzed and error estimates are derived. It is also further, observed that in cases where f = 0 or f = O(e^?γ₀t) with γ₀ > 0, the discrete solutions and error estimates decay exponentially in time. Finally, some numerical experiments are discussed which confirm our theoretical findings.     

Maximum Likelihood Estimators in a Statistical Model of Natural Catastrophe Claims with Trend

A statistical model to analyse stochastically increasing claims arising out of natural catastrophes is presented. Based on record values, the exponential trends over time can be identified. A more specific three-parameter model involving such a trend is also proposed. Observed claims are modeled as a stochastically increasing sequence of Fréchet distributed random variables. Consistency and asymptotic normality of the joint maximum likelihood estimator are shown. Possible applications in forecasting of claims are indicated. In particular claims data from U.S. hurricanes and Japanese taifuns are discussed. AMS 2000 subject classifications. Primary—62P05, 62F12, Secondary—62H12