普通似然及经验似然情况下的结点问题

本文在普通似然及经验似然情况下,分别对数据无结点和有结点的情况做了计算,得出在普通似然及经验似然问题中,有结点与无结点情况完全相同的结论。     

微观计量分析中缺失数据的极大似然估计

微观计量经济分析中常常遇到缺失数据，传统的处理方法是删除所要分析变量中的缺失数据，或用变量的均值替代缺失数据，这种方法经常造成样本有偏。极大似然估计方法可以有效地处理和估计缺失数据。本文首先介绍缺失数据的极大似然估计方法，然后对一实际调查数据中的缺失数据进行极大似然估计，并与传统处理方法的估计结果进行比较和评价。     

逐次定数截尾下Weibull分布参数的逆矩估计

基于逐次定数截尾样本下,讨论了两参数Weibull分布的参数估计,得到了两参数的逆矩估计.并利用模拟方法与极大似然估计作比较,模拟结果表明逆矩估计优于极大似然估计。     

GARCH模型的经验似然统计方法

文章考察经验似然方法在GARCH模型的应用,运用经验似然方法来构造服从卡方分布的经验似然比统计量,进而构造其置信区间,最后通过数值模拟来说明经验似然应用于GARCH模型的优良性。     

基于定数截尾样本的指数分布的环境因子估计

讨论了定数截尾样本下,指数分布环境因子的极大似然估计和区间估计,为研究估计的精度,运用随机模拟方法,对环境因子的置信区间的精度进行了讨论。     

空间动态面板模型拟极大似然估计的渐近效率改进

Lee和Yu(2008)研究了一类同时带个体与时间固定效应的空间动态面板模型的拟极大似然估计量的大样本性质.本文说明当扰动项非正态时,拟极大似然估计量的渐近效率可以被进一步提高.为此,我们构造了一组合待定矩阵且形式一般的矩条件以用来包含对数似然函数一阶条件的特殊形式.从无冗余矩条件的角度,选取最优待定矩阵得到了最佳广义矩估计量.本文证明了当扰动项正态分布时,最佳广义矩估计量和拟极大似然估计量渐近等价;当扰动项非正态分布时,广义矩估计量具有比拟极大似然估计量更高的渐近效率.Monte Carlo实验结果与本文的理论预期一致.     

半参数变系数空间滞后模型的截面极大似然估计

在线性参数空间滞后模型中,解释变量的系数一般假设为固定常数,本文首先放松了这种假设,将解释变量的系数设定为某一变量的未知函数,提出一类全新的半参数变系数空间滞后模型;其次导出了该模型的截面极大似然估计,并证明了该估计的一致性;最后用蒙特卡洛数值模拟方法考察了该估计在小样本条件下的性质,数值模拟结果显示我们提出的估计方法在小样本条件下依然有优良的表现。     

非参数核密度估计在异方差模型中的应用

针对非参数核密度估计中最优窗宽的选择在实际建模中的不足,提出了一个新的最优窗宽选择的迭代方法,克服了使用传统的经验法则所带来的局限性。并在此基础上用一种新的非参数核密度估计ML方法应用到了中国股票市场,通过与极大似然估计对比论证了此方法的有效性和可行性。实证分析表明,通过与实际值的模拟对比,运用非参数估计技术得到上证指数日收益率的拟合值要优于极大似然估计的拟合值。     

锥序约束下定数截尾情形两指数总体均值的估计及性质

本文给出了在定数截尾情形,在锥序约束α1λ1≤λ2≤α2λ1,α1＞0,α2＞0,α1≤α2条件下,两指数总体均值λ的约束极大似然估计λi,i=1,2。证明了λi具有比常用估计量Si更小的均方误差,并且给出了λi对Si的渐进效率,i=1,2。     

一种估计和检验排序模型中结构变化的方法及应用

研究目标：给出一种估计和检验排序模型中结构变化的方法。研究方法：在排序模型中引入平滑转换函数来描述结构变化,在此基础上构建拉格朗日乘子统计量检验模型中的结构变化,并使用极大似然方法估计模型。研究发现：拉格朗日乘子统计量具有标准的渐近卡方分布,并且该统计量对误差项的不同分布形式具有较好的稳健性;极大似然估计量具有一致性和渐近正态性;应用本文的方法分析居民收入和幸福关系,发现收入对幸福的影响存在显著的非线性结构变化特征,当收入增长超过社会收入分布的80%分位数时,收入对幸福的作用会减弱。研究创新：提出了一种新的并且是比较简便的估计和检验排序模型中结构变化的方法。研究价值：这种新的方法可以广泛应用于主观评价问题中的结构变化分析。     

On solving bias‐corrected non‐linear estimation equations with an application to the dynamic linear model

In a seminal paper, Mak, Journal of the Royal Statistical Society B, 55, 1993, 945, derived an efficient algorithm for solving non‐linear unbiased estimation equations. In this paper, we show that when Mak's algorithm is applied to biased estimation equations, it results in the estimates that would come from solving a bias‐corrected estimation equation, making it a consistent estimator if regularity conditions hold. In addition, the properties that Mak established for his algorithm also apply in the case of biased estimation equations but for estimates from the bias‐corrected equations. The marginal likelihood estimator is obtained when the approach is applied to both maximum likelihood and least squares estimation of the covariance matrix parameters in the general linear regression model. The new approach results in two new estimators when applied to the profile and marginal likelihood functions for estimating the lagged dependent variable coefficient in the dynamic linear regression model. Monte Carlo simulation results show the new approach leads to a better estimator when applied to the standard profile likelihood. It is therefore recommended for situations in which standard estimators are known to be biased.     

Conditional empirical likelihood estimation and inference for quantile regression models

This paper considers two empirical likelihood-based estimation, inference, and specification testing methods for quantile regression models. First, we apply the method of conditional empirical likelihood (CEL) by Kitamura et al. [2004. Empirical likelihood-based inference in conditional moment restriction models. Econometrica 72, 1667–1714] and Zhang and Gijbels [2003. Sieve empirical likelihood and extensions of the generalized least squares. Scandinavian Journal of Statistics 30, 1–24] to quantile regression models. Second, to avoid practical problems of the CEL method induced by the discontinuity in parameters of CEL, we propose a smoothed counterpart of CEL, called smoothed conditional empirical likelihood (SCEL). We derive asymptotic properties of the CEL and SCEL estimators, parameter hypothesis tests, and model specification tests. Important features are (i) the CEL and SCEL estimators are asymptotically efficient and do not require preliminary weight estimation; (ii) by inverting the CEL and SCEL ratio parameter hypothesis tests, asymptotically valid confidence intervals can be obtained without estimating the asymptotic variances of the estimators; and (iii) in contrast to CEL, the SCEL method can be implemented by some standard Newton-type optimization. Simulation results demonstrate that the SCEL method in particular compares favorably with existing alternatives.     

Three Sides of Smoothing: Categorical Data Smoothing, Nonparametric Regression, and Density Estimation

The past forty years have seen a great deal of research into the construction and properties of nonparametric estimates of smooth functions. This research has focused primarily on two sides of the smoothing problem: nonparametric regression and density estimation. Theoretical results for these two situations are similar, and multivariate density estimation was an early justification for the Nadaraya-Watson kernel regression estimator.
A third, less well-explored, strand of applications of smoothing is to the estimation of probabilities in categorical data. In this paper the position of categorical data smoothing as a bridge between nonparametric regression and density estimation is explored. Nonparametric regression provides a paradigm for the construction of effective categorical smoothing estimates, and use of an appropriate likelihood function yields cell probability estimates with many desirable properties. Such estimates can be used to construct regression estimates when one or more of the categorical variables are viewed as response variables. They also lead naturally to the construction of well-behaved density estimates using local or penalized likelihood estimation, which can then be used in a regression context. Several real data sets are used to illustrate these points.     

Parameter estimation for the drift of a time inhomogeneous jump diffusion process

This work deals with parameter estimation for the drift of jump diffusion processes which are driven by a Lévy process and whose drift term is linear in the parameter. In contrast to the commonly used maximum likelihood estimator, our proposed estimator has the practical advantage that its calculation does not require the evaluation of the continuous part of the sample path. In the important case of an Ornstein‐Uhlenbeck‐type jump diffusion, which is a widely used model, we prove consistency and asymptotic normality.     

Estimating structural equation models with non-normal variables by using transformations

We discuss structural equation models for non-normal variables. In this situation the maximum likelihood and the generalized least-squares estimates of the model parameters can give incorrect estimates of the standard errors and the associated goodness-of-fit chi-squared statistics. If the sample size is not large, for instance smaller than about 1000, asymptotic distribution-free estimation methods are also not applicable. This paper assumes that the observed variables are transformed to normally distributed variables. The non-normally distributed variables are transformed with a Box–Cox function. Estimation of the model parameters and the transformation parameters is done by the maximum likelihood method. Furthermore, the test statistics (i.e. standard deviations) of these parameters are derived. This makes it possible to show the importance of the transformations. Finally, an empirical example is presented.     

Analysis of Categorical Data for Complex Surveys

This paper reviews methods for handling complex sampling schemes when analysing categorical survey data. It is generally assumed that the complex sampling scheme does not affect the specification of the parameters of interest, only the methodology for making inference about these parameters. The organisation of the paper is loosely chronological. Contingency table data are emphasised first before moving on to the analysis of unit‐level data. Weighted least squares methods, introduced in the mid 1970s along with methods for two‐way tables, receive early attention. They are followed by more general methods based on maximum likelihood, particularly pseudo maximum likelihood estimation. Point estimation methods typically involve the use of survey weights in some way. Variance estimation methods are described in broad terms. There is a particular emphasis on methods of testing. The main modelling methods considered are log‐linear models, logit models, generalised linear models and latent variable models. There is no coverage of multilevel models.     

Estimating and testing linkage disequilibrium from sib data

We consider estimation and testing of linkage equilibrium from genotypic data on a random sample of sibs, such as monozygotic and dizygotic twins. We compute the maximum likelihood estimator with an EM‐algorithm and a likelihood ratio statistic that takes the family structure into account. As we are interested in applying this to twin data we also allow observations on single children, so that monozygotic twins can be included. We allow non‐zero recombination fraction between the loci of interest, so that linkage disequilibrium between both linked and unlinked loci can be tested. The EM‐algorithm for computing the maximum likelihood estimator of the haplotype frequencies and the likelihood ratio test‐statistic, are described in detail. It is shown that the usual estimators of haplotype frequencies based on ignoring that the sibs are related are inefficient, and the likelihood ratio test for testing that the loci are in linkage disequilibrium.     

On the estimation of the parameters for the Littlewood model in software reliability

A very well-known model in software reliability theory is that of Littlewood (1980). The (three) parameters in this model are usually estimated by means of the maximum likelihood method. The system of likelihood equations can have more than one solution. Only one of them will be consistent, however. In this paper we present a different, more analytical approach, exploiting the mathematical properties of the log-likelihood function itself. Our belief is that the ideas and methods developed in this paper could also be of interest for statisticians working on the estimation of the parameters of the generalised Pareto distribution. For those more generally interested in maximum likelihood the paper provides a 'practical case', indicating how complex matters may become when only three parameters are involved. Moreover, readers not familiar with counting process theory and software reliability are given a first introduction.