非线性模型中的拟似然估计和约束拟似然估计

该文证明了,在非线性回归模型中,若以均方误差或均方误差矩阵为标准,拟似然估计是正则广义拟似然估计类中的最优估计,并讨论了拟得分函数最优性与拟似然估计最优性的关系.为改进拟似然估计,该文提出了一种约束拟似然估计,并证明了约束拟似然估计比拟似然估计有较小的均方误差.     

基于多维名义模型的加权似然估计方法(英文)

The Monte Carlo study evaluates the relative accuracy of Warm's (1989) weighted likelihood estimate (WLE) compared to the maximum likelihood estimate (MLE) using the nominal response model. And the results indicate that WLE was more accurate than MLE.     

最大似然估计的一个推广

我们常常会遇到最大似然估计不存在的情况,这种情况以在非正态回归模型中最为典型。当参数向量不能被估计时,人们对参数向量的线性函数的估计饶有兴趣。本文给出了这些线性函数的广义最大似然估计的定义,讨论了它的性质,并得到了利用投影变换确定具有有限广义最大似然估计的线性函数的方法。最后,通过几个常见的定性资料统计模型的实例,展现了求广义最大似然估计的实施过程。     

Logistic回归模型的经验似然诊断

经验似然方法已经被广泛用于许多模型的统计推断.基于经验似然对Logistic回归模型进行统计诊断.首先给出模型的估计方程,进而得到模型参数的极大经验似然估计;其次,基于经验似然研究了三种不同的影响曲率;最后通过实例分析,说明了统计诊断方法的有效性.     

非线性联立方程模型的充分信息最大加权似然估计及其性质

提出非线性联立方程模型的充分信息最大加权似然估计并得到其一致性和渐近正态性的大样本性质 .     

相依非线性回归系统中的附加信息Bayes拟似然

对多个相依统计模型的研究,现有成果主要集中在相依线性回归系统.本文则首次提出多个相依非线性回归系统中的附加信息Bayes拟似然,给出误差相关信息和先验信息在拟似然中的迭加方法,在较弱的条件下得到附加信息Bayes拟似然的一些性质,在Bayes风险准则下。讨论了其估计函数和参数估计的最优性,证明了附加信息Bayes拟似然的渐近 Bayes风险随着相依信息的增力。而逐步减少.     

向量参数的线性函数之广义最大似然估计

最大似然估计不存在的情况在非正态回归模型中最为典型,当参数向量不能被估计时,人们对参数向量的线性函数的估计饶有兴趣。本文给出了这些线性函数的广义最大似然 定义,建立了一些关于凹目标函数的结果,对某些特殊的目标函数,提供了求广义最大似然估计的具体途径,并详细地考虑了Ｃｏｘ的生存时间分析的模型。     

用Excel软件实现最大似然估计数值计算的方法

本文给出用Excel软件实现最大似然估计数值计算求解的方法。内容包括对似然方程求数值解、直接对似然函数或对数似然函数求极大值以及分组数据最大似然估计的数值计算。     

基于经验似然的部分线性模型的统计诊断

经验似然方法己经被广泛应用于许多模型的统计推断.本文基于经验似然对部分线性模型进行统计诊断.首先给出模型的估计方程,进而得到模型参数的极大经验似然估计;其次,基于经验似然研究了三种不同的影响曲率;最后通过随机模拟和实例分析,说明了统计诊断方法的有效性.     

MA$(q)$模型的经验似然推断

In this article we study the empirical likelihood inference for MA（q） model. We propose the moment restrictions, by which we get the empirical likelihood estimator of the model parameter, and we also propose an empirical log-likelihood ratio based on this estimator. Our result shows that the EL estimator is asymptotically normal, and the empirical log-likelihood ratio is proved to be asymptotical standard chi-square distribution.     

Maximum Kernel Likelihood Estimation

We introduce an estimator for the population mean based on maximizing likelihoods formed by parameterizing a kernel density estimate. Due to these origins, we have dubbed the estimator the maximum kernel likelihood estimate (MKLE). A speedy computational method to compute the MKLE based on binning is implemented in a simulation study which shows that the MKLE at an optimal bandwidth is decidedly superior in terms of efficiency to the sample mean and other measures of location for heavy tailed symmetric distributions. An empirical rule and a computational method to estimate this optimal bandwidth are developed and used to construct bootstrap confidence intervals for the population mean. We show that the intervals have approximately nominal coverage and have significantly smaller average width than the standard t and z intervals. Finally, we develop some mathematical properties for a very close approximation to the MKLE called the kernel mean. In particular, we demonstrate that the kernel mean is indeed unbiased for the population mean for symmetric distributions.     

广义线性回归极大似然估计的强相合性

设有该文第1节所描述的广义线性回归模型,以$\underline{\lambda}_n$和$\overline{\lambda}_n$分别记$\sum\limits_{i=1}^{n}Z_iZ_i^{\prime}$的最小和最大特征根,$\hat{\beta}_n$记$\beta_0$的极大似然估计.在文献[1]中,当\{$Z_i,i\ge1$\}有界时得到$\hat{\beta}_n$强相合的充分条件,在自然联系和非自然联系下分别为$\underline{\lambda}_n\rightarrow\infty$, $(\overline{\lambda}_n)^{1/2+\delta}=O(\underline{\lambda}_n)$（对某$\delta>0$)以及$\underline{\lambda}_n\rightarrow\infty$, $\overline{\lambda}_n=O(\underline{\lambda}_n)$.作者将后一结果改进为只要求$(\overline{\lambda}_n)^{1/2+\delta}=O(\underline{\lambda}_n)$,从而与自然联系情况下的条件达到一致.     

多项Probit模型参数的极大似然估计

本文考虑多项probit模型中参数的极大似然估计(MLE)的存在性.在协方差阵已知和均匀结构两种情况下,给出MLE存在的充要条件.     

多周期Probit模型中MLE的存在性

本文我们讨论了多周期Probit模型中MLE的存在性问题,给出了当协方差阵已知时,参数的MLE存在的充要条件;当协方差阵未知但具有序列结构时,参数的MLE存在的一个必要条件和一个充分条件.     

具有Rao简单结构的多元t-模型的MLE及其精确分布

探求模型中未知参数的估计及其分布一直是统计学研究中的感兴趣的问题.本文研究了具有Rao简单结构多元t-模型的极大似然估计, 利用条件分布方法,获得了其精确分布.     

Efficient Algorithm for Computing Maximum Likelihood Estimates in Linear Transformation Models

Linear transformation models, which have been extensively studied in survival analysis, include the two special cases: the proportional hazards model and the proportional odds model. Nonparametric maximum likelihood estimation is usually used to derive the efficient estimators. However, due to the large number of nuisance parameters, calculation of the nonparametric maximum likelihood estimator is difficult in practice, except for the proportional hazards model. We propose an efficient algorithm for computing the maximum likelihood estimates, where the dimensionality of the parameter space is dramatically reduced so that only a finite number of equations need to be solved. Moreover, the asymptotic variance is automatically estimated in the computing procedure. Extensive simulation studies indicate that the proposed algorithm works very well for linear transformation models. A real example is presented for an illustration of the new methodology.     

Parameter Estimation in Hidden Markov Models With Intractable Likelihoods Using Sequential Monte Carlo

We propose sequential Monte Carlo-based algorithms for maximum likelihood estimation of the static parameters in hidden Markov models with an intractable likelihood using ideas from approximate Bayesian computation. The static parameter estimation algorithms are gradient-based and cover both offline and online estimation. We demonstrate their performance by estimating the parameters of three intractable models, namely the α-stable distribution, g-and-k distribution, and the stochastic volatility model with α-stable returns, using both real and synthetic data.     

线性度量误差模型的极大经验似然估计

本文将自变量的测量误差考虑到线性模型中,提出了线性度量误差模型参数的极大经验似然估计,在一定条件下,证明了所得到的未知参数的估计具有渐进正态性,并通过数值模拟,说明了该方法的可行性。     

具有Rao简单结构的多元t-模型的MLE的数字特征

本文在文[7]已求得未知参数MLEs的基础上，利用条件期望方法，研究了具有Rao简单结构多元t-模型的极大似然估计的数字特征．     

Sharp Error Estimate for Maximum Likelihood Estimator of Nonstationary Diffusion Processes

We consider the maximum likelihood estimator of the unknown parameter in a class of nonstationary diffusion processes. We give further a precise estimate for the error of the estimator.