Modified Maximum Likelihood Estimators Based on Ranked Set Samples

The maximum livelihood estimator (MLE) using a ranked set sample (RSS) usually has no closed expression because the maximum likelihood equation involves both hazard and inverse hazard functions, and may no longer be efficient when the judgment ranking is imperfect. In this paper, we consider a modified MLE (MMLE) using RSS for general parameters, which has the same expression as the MLE using a simple random sample (SRS), except that the SRS in the MLE is replaced by the RSS. The results show that, for the location parameter, the MMLE is always more efficient than the MLE using SRS, and for the scale parameter, the MMLE is at least as efficient as the MLE using SRS, when the same sample size is used. Under the perfect judgment ranking, numerical examples also show that the MMLE has good efficiency relative to the MLE based on RSS. When the judgment error is present, we conduct simulations to show that the MMLE is more robust than the MLE using RSS.     

带有不完全信息随机截尾试验下参数MLE的重对数律

在条件(Ψ)下,证明了带有不完全信息随机截尾试验中参数MLE的收敛速度符合重对数律,并且验证了指数分布、Weibull分布、对数正态分布满足条件(Ψ).     

A Comparison of Restricted and Unrestricted Estimators in Estimating Linear Functions of Ordered Scale Parameters of Two Gamma Distributions

The problem of estimating linear functions of ordered scale parameters of two Gamma distributions is considered. A necessary and sufficient condition on the ratio of two coefficients is given for the maximum likelihood estimator (MLE) to dominate the crude unbiased estimator (UE) in terms of mean square error. A modified MLE which satisfies the restriction is also suggested, and a necessary and sufficient condition is also given for it to dominate the admissible estimator based solely on one sample. The estimation of linear functions of variances in two sample problem and also of variance components in a one-way random effect model is mentioned.     

A coding problem in steganography

To study how to design a steganographic algorithm more efficiently, a new coding problem—steganographic codes (abbreviated stego-codes)—is presented in this paper. The stego-codes are defined over the field with q(q ≥ 2) elements. A method of constructing linear stego-codes is proposed by using the direct sum of vector subspaces. And the problem of linear stego-codes is converted to an algebraic problem by introducing the concept of the tth dimension of a vector space. Some bounds on the length of stego-codes are obtained, from which the maximum length embeddable (MLE) code arises. It is shown that there is a corresponding relation between MLE codes and perfect error-correcting codes. Furthermore the classification of all MLE codes and a lower bound on the number of binary MLE codes are obtained based on the corresponding results on perfect codes. Finally hiding redundancy is defined to value the performance of stego-codes.      

基于分组数据的回归系数的估计

本文讨论了如何去解决基于分组数据下的回归系数的估计问题.本文所讨论的基于分组数据下的回归模型与经典回归模型的差异在于因变量的观测值为分组数据,即我们只知道它落于事先确定的一组区间中的某一区间,而不知道它的具体值;而经典回归模型的因变量观测值则是一个确定的数值.我们用MLE去估计回归系数,但是此时的MLE无显式解,所以寻找一个合适的迭代算法就成了问题的关键.我们选择利用Bayes计算方法中的EM算法来获得估计量的迭代公式.随机模拟显示了所得估计的有效性.     

一种改进的半参数极大似然法估计量的渐近性质

本文研究线性回归模型, Y=β'X+∈,并假设Y可被右删失,∈的分布函 数F0未知.本文证明,在某些条件下, β的一种改进的半参数极大似然法估计量β 有相合性. 同时证明,如果F0不连续,则P{β≠βi.o.}=0.这意味着以概率为一, 当样本很大时, β=β.文献中的现有估计量未见有关于这一性质的报道.相反,包括 Buckley-James估计量及M-估计量在内的大多数的估计量,都不满足这一性质.     

不完全信息随机截尾模型的MLE 的Chung 重对数律

在一定条件下,证明不完全信息随机截尾模型的MLE 满足 Chung重对数律. 作为其推论得到:不完全信息随机截尾试验下,指数分布和Weibull 分布的MLE 满足Chung 重对数律.     

Kullback-Leibler Information Consistent Estimation for Censored Data

This paper is intended as an investigation of parametric estimation for the randomly right censored data. In parametric estimation, the Kullback-Leibler information is used as a measure of the divergence of a true distribution generating a data relative to a distribution in an assumed parametric model M. When the data is uncensored, maximum likelihood estimator (MLE) is a consistent estimator of minimizing the Kullback-Leibler information, even if the assumed model M does not contain the true distribution. We call this property minimum Kullback-Leibler information consistency (MKLI-consistency). However, the MLE obtained by maximizing the likelihood function based on the censored data is not MKLI-consistent. As an alternative to the MLE, Oakes (1986, Biometrics, 42, 177–182) proposed an estimator termed approximate maximum likelihood estimator (AMLE) due to its computational advantage and potential for robustness. We show MKLI-consistency and asymptotic normality of the AMLE under the misspecification of the parametric model. In a simulation study, we investigate mean square errors of these two estimators and an estimator which is obtained by treating a jackknife corrected Kaplan-Meier integral as the log-likelihood. On the basis of the simulation results and the asymptotic results, we discuss comparison among these estimators. We also derive information criteria for the MLE and the AMLE under censorship, and which can be used not only for selecting models but also for selecting estimation procedures.     

Asymptotic Properties of a Modified Semi-Parametric MLE in Linear Regression with Right-Censored Data

Consider a linear regression model, Y=β′X+ε where Y may be right censored and the cdf F _o of ε is unknown. We show that a modified semi-parametric MLE, denoted by is strongly consistent under certain regularity conditions. Moreover, if F _o is discontinuous, then P(≠β i.o.)=0, which means that P(=β if the sample size is large)=1. The latter property has not been reported for the existing estimators. By contrast, most estimators, such as the Buckley-James estimator and M-estimators , satisfy that P(≠β i.o.)=1. Received April 23, 2001, Accepted November 13, 2001     

Joint modeling of cointegration and conditional heteroscedasticity with applications

A cointegrated vector AR-GARCH time series model is introduced. Least squares estimator, full rank maximum likelihood estimator (MLE), and reduced rank MLE of the model are presented. Monte Carlo experiments are conducted to illustrate the finite sample properties of the estimators. Its applicability is then demonstrated with the modeling of international stock indices and exchange rates. The model leads to reasonable financial interpretations.     

分组数据下参数极大似然估计渐近有效性

当数据为分组型时,本文证明了一般分布的参数的极大似然估计具有指数收敛速度,并具有Bahadur渐近有效性.     

截尾寿命试验中参数最大似然估计的重对数律

本文对于包含定数和定时截尾寿命试验的混合型寿命试验，研究了分布参数的最大似然估计．基于截尾数据，证明了最大似然估计的收敛速度符合重对数律．     

Reducing bias of the maximum likelihood estimator of shape parameter for the gamma Distribution

The gamma distribution is an important probability distribution in statistics. The maximum likelihood estimator (MLE) of its shape parameter is well known to be considerably biased, so that it has some modified versions. A new modified MLE of the shape for the gamma distribution is proposed in this paper, which is consistent, asymptotically normal and efficient. For finite-sample behavior, the new estimator improves the traditional MLE not only for reducing bias but also for gaining estimation efficiency significantly. In terms of estimation efficiency, it dominates other existing modified estimators.     

Censored regression analysis of multiclass passenger demand data subject to joint capacity constraints

In most passenger transportation systems, demand for seats is not recorded after all spaces for a particular trip have been sold out or after a booking limit has been reached. Thus historical booking data is comprised of ticketsales notdemand — a condition known as censorship of the data. Data censorship is particularly complex when there are multiple classes of demand since the demand in one class can influence the degree of censorship in another. This paper examines the problem of simultaneously estimating passenger demand models for two or more correlated classes of demand that are subject to a common capacity constraint. It is shown that theEM method of Dempster et al. [5] can be adapted to provide maximum likelihood estimates of the parameters of the demand model under these circumstances. The problem of modelling demand for airline flights is discussed as a typical example of this estimation problem. Numerical examples show that, with reasonable sample sizes, it is possible to obtain good estimates even when 75% or more of the data have been censored.     

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。     

New estimating equation approaches with application in lifetime data analysis

Estimating equation approaches have been widely used in statistics inference. Important examples of estimating equations are the likelihood equations. Since its introduction by Sir R. A. Fisher almost a century ago, maximum likelihood estimation (MLE) is still the most popular estimation method used for fitting probability distribution to data, including fitting lifetime distributions with censored data. However, MLE may produce substantial bias and even fail to obtain valid confidence intervals when data size is not large enough or there is censoring data. In this paper, based on nonlinear combinations of order statistics, we propose new estimation equation approaches for a class of probability distributions, which are particularly effective for skewed distributions with small sample sizes and censored data. The proposed approaches may possess a number of attractive properties such as consistency, sufficiency and uniqueness. Asymptotic normality of these new estimators is derived. The construction of new estimation equations and their numerical performance under different censored schemes are detailed via Weibull distribution and generalized exponential distribution.     

A new generalized linear exponential distribution and its applications

A new generalized linear exponential distribution （NCLED） is considered in this paper which can be deemed as a new and more flexible extension of linear exponential distribution. Some statistical properties for the NGLED such as the hazard rate function, moments, quantiles are given. The maximum likelihood estimations （MLE） of unknown parameters are also discussed. A simulation study and two real data analyzes are carried out to illustrate that the new distribution is more flexible and effective than other popular distributions in modeling lifetime data.     

Gamma分布环境因子的统计分析

证明了Gamma分布环境因子的最大似然估计是有偏估计,且其偏差为正,进而导出了Gamma分布环境因子的近似无偏估计.利用Cornish-Fisher展开导出了Gamma分布环境因子的广义置信区间,另外也给了Gamma分布环境因子的Bootstrap-t置信区间.利用模拟方法研究了所给近似无偏估计和区间估计的精度,模拟结果显示所给近似无偏估计和区间估计的精度是相当好的.     

带有不完全信息随机截尾试验下最大似然估计的重对数律

本文在条件($\Phi$)下,证明了带有不完全信息随机截尾试验下最大似然估计的收敛速度符合重对数律,并验证了Weibull分布、对数正态分布满足条件($\Phi$).     

Ⅰ型区间删失情形下部分线性模型Sieve极大似然估计渐近性质

本文在响应变量的观测值为Ⅰ型区间删失数据的情形下,讨论部分线性模型Ｓｉｅｖｅ极大似然估计的渐近性质．在一定条件下证明了该估计具有强相合性;参数分量的估计具有渐近正态性,并且是渐近有效的;非参数分量估计达到了最优弱收敛速度．