改进的Gompertz模型参数估计方法比较研究

讨论改进的Gompertz模型两种参数估计方法:三和法和非线性最小二乘估计法,并通过蒙特卡洛实验比较两种估计方法的精度和收敛率,得出非线性最小二乘估计法在估计精度和估计的成功率两方面都优于三和法的结论;利用Gompertz曲线拟合中国电影票房数据并对其未来发展作出预测:中国电影票房最终可以在2025年左右到达饱和状态,饱和状态总规模大约为1 676.5亿元。     

Exponentiated Chen distribution: Properties and estimation

This article addresses various properties and estimation methods for the Exponentiated Chen distribution. Although, our main focus is on estimation from frequentist point of view, yet, some statistical and reliability characteristics for the model are derived. We briefly describe different estimation procedures, namely, the method of maximum likelihood estimation, percentile estimation, least square and weighted least-square estimation, maximum product of spacings estimation, Cramér-von-Mises estimation, Anderson–Darling, and right-tail Anderson–Darling estimation. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, the potentiality of the model is analyzed by means of three real datasets.     

Estimation procedures for grouped data – a comparative study

Interval-censored data are very common in the reliability and lifetime data analysis. This paper investigates the performance of different estimation procedures for a special type of interval-censored data, i.e. grouped data, from three widely used lifetime distributions. The approaches considered here include the maximum likelihood estimation, the minimum distance estimation based on chi-square criterion, the moment estimation based on imputation (IM) method and an ad hoc estimation procedure. Although IM-based techniques are extensively used recently, we show that this method is not always effective. It is found that the ad hoc estimation procedure is equivalent to the minimum distance estimation with another distance metric and more effective in the simulation. The procedures of different approaches are presented and their performances are investigated by Monte Carlo simulation for various combinations of sample sizes and parameter settings. The numerical results provide guidelines to analyse grouped data for practitioners when they need to choose a good estimation approach.     

A resisting gross errors capability study of robust estimation of unary linear regression method

Robust estimation methods are often used to eliminate or weaken the influences of gross errors on parameter estimation. However, different robust estimation methods may have different capabilities in eliminating or weakening gross errors. Taking unary linear regression as example, simulation experiments are used to compare 14 frequently used robust estimation methods. The current article summarizes the common characteristics and rules of the robust estimation methods. Finally, we confirm several relatively more efficient methods for unary linear regression.     

问卷分割设计的模拟研究——小域估计的一种应用

针对长问卷存在无回答率和回答负担,从而导致统计调查精度降低的问题,采用问卷分割法解决该问题,并且通过小域估计的方法进行参数估计。模拟研究表明,利用小域估计方法对分割问卷进行参数估计显然优于用多重插补法进行参数估计。研究结果表明,运用小域估计方法对分割问卷进行参数估计,能显著提高统计调查的精度。     

Comparison of Ability Estimation Methods Using IRT for Tests with Different Degrees of Difficulty

The aim of the present study is to determine the dependence of the estimation of individual abilities obtained by item response theory (IRT) in relation to the degree of test difficulty and to evaluate how the estimation error may be affected by the estimation method employed. It is shown that abilities in the scale region with little test information are more efficiently estimated using the maximum weighted likelihood estimation (WLE) method, particularly abilities belonging to the upper part of the scale. The study also demonstrates the importance of largest tests for ability estimation.     

An example of applying the asymptotic quasi-likelihood to dimension estimation for random spatial patterns

With reference to a specific example of a random spatial fractal and the modified box-counting method of dimension estimation, this paper aims to examine firstly the estimation of pointwise dimension via modification of the box-counting procedure, secondly the regression inspired estimation procedure, including generalised least squares and, finally, to develop a new estimation procedure – the asymptotic quasi-likelihood method – for the estimation of pointwise dimension. The main focus is on practicality – to arrive at an estimation method which is easy to use and robust.     

Efficiently weighted estimating equations with application to proportional excess hazards

A general approach to estimation, that can lead to efficient estimation in two stages, is presented. The method will not always be available, but sufficient conditions for efficiency are provided together with four examples of its use: (1) estimation of the odds ratio in 1:M matched case-control studies with a dichotomous exposure variable; (2) estimation of the relative hazard in a two-sample survival setting; (3) estimation of the regression parameters in the proportional excess hazards model; and (4) estimation in a partly linear parametric additive hazards model. The method depends upon finding a family of weighted estimating equations, which includes a simple initial equation yielding a consistent estimate and also an equation that yields an efficient estimate, provided the optiomal weights are used.     

基于多重抽样框的校准估计方法研究

在现代抽样调查中,校准估计方法能够通过有效利用辅助信息来提高估计量的精度,多重抽样框抽样调查则不仅可以解决单一抽样框覆盖不全的问题,还可以节约抽样设计阶段的成本。本文将这两种现代抽样估计与设计方法进行结合,将校准估计方法引入到基于多重抽样框的抽样调查体系中,在实现节约调查成本的同时,还能够提高估计量的精度。文章首先按照分离抽样框与组合抽样框估计方法的分类思路,对传统多重抽样框估计方法进行系统梳理;然后在最短距离法校准估计的分析框架下,按照调查时所能掌握辅助信息的具体情况,给出了两类多重抽样框估计情形下的各种不同形式的校准估计量;随后数值分析的比较结果也表明在多重抽样框中校准估计量的估计效率明显优于传统估计量;最后对本文研究进行总结的基础上,给出了我国抽样实践中应用这套先进抽样估计方法体系的展望。     

A practical method for analysing heavy tailed data

An important practical issue of applying heavy tailed distributions is how to choose the sample fraction or threshold, since only a fraction of upper order statistics can be employed in the inference. Recently, Guillou & Hall ( 2001 ; Journal of Royal Statistical Society B, 63, 293–305) proposed a simple way to choose the threshold in estimating a tail index. In this article, the author first gives an intuitive explanation of the approach in Guillou & Hall ( 2001 ; it Journal of Royal Statistical Society B, 63, 293–305) and then proposes an alternative method, which can be extended to other settings like extreme value index estimation and tail dependence function estimation. Further the author proposes to combine this method for selecting a threshold with a bias reduction estimator to improve the performance of the tail index estimation, interval estimation of a tail index, and high quantile estimation. Simulation studies on both point estimation and interval estimation for a tail index show that both selection procedures are comparable and bias reduction estimation with the threshold selected by either method is preferred. The Canadian Journal of Statistics © 2009 Statistical Society of Canada     

空间ZISF的估计及蒙特卡罗模拟

在随机前沿模型中引入空间效应和技术无效率项的非连续性并构建了空间零无效率随机前沿模型,使用极大似然估计和JLMS方法得出参数和技术效率的估计。蒙特卡罗模拟表明:(1)逆似然比检验能以较高的准确率识别真实模型;(2)本方法在参数估计和技术效率的估计两方面均表现较好;(3)若真实模型为空间零无效率随机前沿模型但误用了空间随机前沿模型,参数估计和技术效率的估计两方面均表现较差。空间零无效率随机前沿模型有其存在的必要性。     

A natural conjugate prior for the non-homogeneous poisson process with a power law intensity function

This paper develops a natural conjugate prior for the non-homogeneous Poisson process (NHPP) with a power law intensity function. This prior allows for dependence between the scale factor and the aging rate of the NHPP. The proposed prior has relatively simple closed-form expressions for its moments, facilitating the assessment of prior parameters. The use of this prior in Bayesian estimation is compared to other estimation approaches using Monte Carlo simulation. The results show that Bayesian estimation using the proposed prior generally performs at least as well as either maximum likelihood estimation or Bayesian estimation using independent prior     

Simultaneous estimation for semi-parametric multi-index models

Estimation of a general multi-index model comprises determining the number of linear combinations of predictors (structural dimension) that are related to the response, estimating the loadings of each index vector, selecting the active predictors and estimating the underlying link function. These objectives are often achieved sequentially at different stages of the estimation process. In this study, we propose a unified estimation approach under a semi-parametric model framework to attain these estimation goals simultaneously. The proposed estimation method is more efficient and stable than many existing methods where the estimation error in the structural dimension may propagate to the estimation of the index vectors and variable selection stages. A detailed algorithm is provided to implement the proposed method. Comprehensive simulations and a real data analysis illustrate the effectiveness of the proposed method.     

Data skeletons: simultaneous estimation of multiple quantiles for massive streaming datasets with applications to density estimation

We consider the problem of density estimation when the data is in the form of a continuous stream with no fixed length. In this setting, implementations of the usual methods of density estimation such as kernel density estimation are problematic. We propose a method of density estimation for massive datasets that is based upon taking the derivative of a smooth curve that has been fit through a set of quantile estimates. To achieve this, a low-storage, single-pass, sequential method is proposed for simultaneous estimation of multiple quantiles for massive datasets that form the basis of this method of density estimation. For comparison, we also consider a sequential kernel density estimator. The proposed methods are shown through simulation study to perform well and to have several distinct advantages over existing methods.     

Characterization of an optimal matrix estimator under convex loss function

Characterization of an optimal vector estimator and an optimal matrix estimator are obtained. In each case appropriate convex loss functions are considered. The results are illustrated through the problems of simultaneous unbiased estimation, simultaneous equivariant estimation and simultaneous unbiased prediction. Further an optimality criterion is proposed for matrix unbiased estimation and it is shown that the matrix unbiased estimation of a matrix parametric function and the minimum variance unbiased estimation of its components are equivalent.     

多辅助变量线性组合的回归估计

以提高估计量的精度为目的,定义了一种新的多个辅助变量的回归估计法,从理论上研究了该方法下权的选取方法,并将该方法下的估计量与Raj多辅助变量回归估计量、Ghosh多元线性回归估计量在精度上进行了数值比较,结果表明：这种新的多辅助变量的回归估计法在精度上优于Raj多辅助变量回归估计和Ghosh多元线性回归估计。     

Mean estimation through proportion estimation

In this work a device which changes the problem of mean estimation into that of proportion estimation is proposed. The device consists of perturbing the observations. The goal of the work is the construction of conservative confidence intervals for means. Three applications are given: (1) proportion estimation in the context of cluster random sampling, (2) differences of proportions of a multinomial population and (3) variance estimation.     

分层线性模型的最大后验估计

最大后验估计（MAPE）和最大似然估计（MLE）都是重要的参数点估计方法。在介绍一般分层线性模型（HLM）MAPE方法的基础上,给出这种方法的期望最大化算法（EM）的具体步骤,运用对数似然函数的二阶导数推导了MAPE估计的方差估计量。同时运用数据模拟比较了EM算法下的MAPE和MLE。对于固定效应的估计,两种方法得到的估计量是一致的。当组数较少时,EM计算的MAPE的方差协方差成分比MLE的更靠近真实值,而且MAPE的迭代次数明显小于MLE。     

Nonparametric versus Parametric Estimation of the Cure Fraction Using Interval Censored Data

This article discusses estimation of the cure rate by means of the bounded cumulative hazard (BCH) model using interval censored data. The parametric and nonparametric estimation methods within the framework of the EM algorithm were employed for cure rate estimation and their results compared. The Turnbull estimator was used in the nonparametric estimation while in parametric method both the exponential and Weibull distributions were considered. We show via simulation that the nonparametric method is a viable alternative to the parametric one when the censoring rate is rapidly increasing.     

The E-Bayesian and hierarchical Bayesian estimations for the system reliability parameter

Han introduced an E-Bayesian estimation method for estimating a system failure probability and revealed the relationship between the E-Bayesian estimates under three different prior distributions of hyperparameters in 2007. In this article, formulas of the hierarchical Bayesian estimation of a system failure probability are investigated and, furthermore, the relationship between hierarchical Bayesian estimation and E-Bayesian estimation is discussed. Finally, numerical example and application example are provided for illustrative purpose.