最大似然估计教学中的几点注记

本文总结了最大似然估计教学中容易忽视的一些问题,并对最大似然估计中出现的一些特殊情况进行了举例说明,特别指出不是所有参数都有最大似然估计.     

在截尾样本情形下最大似然估计的强相合性

讨论了在截尾样本情形下最大似然估计的大样本性质，证明了当T＝∞时最大似然估计是强相合的．     

关于最大似然估计的教学

通过浅显事例说明最大似然原理,给出最大似然估计的主要方法。     

一种串联系统可靠性指标的估计

对冷贮备部件串联系统可靠性指标的估计方法进行了研究,提出了最大似然法和经验Bayes估计法,分析结果表明,经验Bayes方法优于最大似然法,估计精度高.     

基于最大L_q似然估计的广义非线性模型的统计诊断(英文)

为了检测数据是否符合给定的模型,需要对数据进行统计诊断.研究了基于最大Lq似然估计的广义非线性模型的统计诊断问题.利用3个统计诊断量来检验数据中是否都存在异常点.模拟结果显示,当样本容量较小时,使用最大Lq似然估计方法得到的诊断统计量的结果要比使用极大似然估计(MLE)方法得到的结果大;随着样本容量的增加,它们之间的区别逐渐减小.因此,使用最大Lq似然估计方法比用MLE方法更容易找到数据中的异常点.     

部分区间删失数据下指数分布中MLE的相合性

部分区间删失数据包括精确数据以及区间删失数据,在慢性病研究中有广泛的应用.本文主要考虑在具有1类部分删失数据下指数分布中最大似然估计的相合性,在一定的正则条件下证明了最大似然估计的强相合性.     

一种时变衰落信道的SNR估计方法

信号噪声比率（SNR）估计是在时变衰落信道环境下相移键控通信系统的重要指标,目前有两种可实现的估计方法：数据辅助估计和非数据辅助估计。时变衰落信道可以建立为一个关于时间的多项式模型。传统的估计方法精度受限于Cramer-Rao下界信道,信道时变特性对于SNR估计的影响可以忽略。目前,一种新颖的最大似然（ML）SNR估计方法是由时变衰落模型推导而来的。对于DA场景估计来说,有一种简易的闭环估计方案,其准确性能评估依赖于正确与错误（不匹配）的多项式阶数。对于NDA估计,未知的数据符号建立为随机的模型,利用了边缘似然估计方法。最大期望算法通过迭代方法使得似然函数最大。仿真结果表明,相比先前公布的算法实现,该估计算法统计效率更高。     

极大似然估计的性质探讨

文章首先介绍了极大似然估计,然后综述了极大似然估计的优良性质,同时探讨了在应用极大似然估计时所应注意的问题。     

在截尾样本情形下最大似然估计的强相合性

摘要讨论了在截尾样本情形下最大似然估计的大样本性质，     

泊松分布中参数的经典估计与Bayes估计的相等关系

文中证明了泊松分布中未知参数的矩估计和最大似然估计,一定存在一个先验分布,使其贝叶斯估计就是该经典估计的结论.     

具有部分缺失数据时两个威布尔分布的估计和检验

文中讨论了部分缺失数据两威布尔总体的参数估计和关于总体相同的似然比检验．证明估计的强相合性和渐近正态性,给出似然比检验统计量的极限分布,并探讨了基于精确分布的检验问题．     

Maximum Likelihood Estimation: for the Multinomial Distribution

In a first course in mathematical statistics or categorical data analysis, the maximum likelihood estimators of the parameters of the multinomial distribution are often “derived” using calculus. However, the important step of verifying that the resulting estimators indeed maximize the likelihood is omitted or done incorrectly. In this paper, two simple methods of obtaining the maximum likelihood estimates are presented.     

Power and Sample Size Calculations for Logistic Regression Tests for Differential Item Functioning

Logistic regression is a popular method for detecting uniform and nonuniform differential item functioning (DIF) effects. Theoretical formulas for the power and sample size calculations are derived for likelihood ratio tests and Wald tests based on the asymptotic distribution of the maximum likelihood estimators for the logistic regression model. The power is related to the item response function (IRF) for the studied item, the latent trait distributions, and the sample sizes for the reference and focal groups. Simulation studies show that the theoretical values calculated from the formulas derived in the article are close to what are observed in the simulated data when the assumptions are satisfied. The robustness of the power formulas are studied with simulations when the assumptions are violated.     

对数正态分布参数的最大似然估计

利用最大似然估计法求出了对数正态分布两个参数的估计量，并讨论了它们的无偏性和相合性。     

逐步Ⅱ型寿命下逆Rayleigh分布参数的估计

在逐步Ⅱ型截尾样本下讨论了逆Rayleigh分布参数的估计问题,给出了参数的最大似然估计,并在三种不同的损失函数下给出了参数的Bayes估计和区间估计.最后给出了数值模拟的例子。     

Performance of Nonrecursive Latent Variable Models under Misspecification

A problem central to structural equation modeling is measurement model specification error and its propagation into the structural part of nonrecursive latent variable models. Full-information estimation techniques such as maximum likelihood are consistent when the model is correctly specified and the sample size large enough; however, any misspecification within the model can affect parameter estimates in other parts of the model. The goals of this study included comparing the bias, efficiency, and accuracy of hypothesis tests in nonrecursive latent variable models with indirect and direct feedback loops. We compare the performance of maximum likelihood, two-stage least-squares and Bayesian estimators in nonrecursive latent variable models with indirect and direct feedback loops under various degrees of misspecification in small to moderate sample size conditions.     

Psychometric Properties of IRT Proficiency Estimates

Psychometric properties of item response theory proficiency estimates are considered in this paper. Proficiency estimators based on summed scores and pattern scores include non-Bayes maximum likelihood and test characteristic curve estimators and Bayesian estimators. The psychometric properties investigated include reliability, conditional standard errors of measurement, and score distributions. Four real-data examples include (a) effects of choice of estimator on score distributions and percent proficient, (b) effects of the prior distribution on score distributions and percent proficient, (c) effects of test length on score distributions and percent proficient, and (d) effects of proficiency estimator on growth-related statistics for a vertical scale. The examples illustrate that the choice of estimator influences score distributions and the assignment of examinee to proficiency levels. In particular, for the examples studied, the choice of Bayes versus non-Bayes estimators had a more serious practical effect than the choice of summed versus pattern scoring.     

Effects of nonnormal data on parameter estimates and fit indices for a model with latent and manifest variables: An empirical study

Research in covariance structure analysis suggests that nonnormal data will invalidate chi‐square tests and produce erroneous standard errors. However, much remains unknown about the extent to and the conditions under which highly skewed and kurtotic data can affect the parameter estimates, standard errors, and fit indices. Using actual kurtotic and skewed data and varying sample sizes and estimation methods, we found that (a) normal theory maximum likelihood (ML) and generalized least squares estimators were fairly consistent and almost identical, (b) standard errors tended to underestimate the true variation of the estimators, but the problem was not very serious for large samples (n = 1,000) and conservative (99%) confidence intervals, and (c) the adjusted chi‐square tests seemed to yield acceptable results with appropriate sample sizes.     

纵向数据下半参数模型估计的渐近正态性

考虑纵向数据半参数回归模型:Y=Xβ+g(T)+ε,基于最小二乘法和局部线性拟合的方法建立了模型中参数分量β,回归函数g(·)和误差方差σ2的估计量,并在适当条件下得到了它们的渐近正态性和最优收敛速度.     

Five Methods for Estimating Angoff Cut Scores with IRT

This article illustrates five different methods for estimating Angoff cut scores using item response theory (IRT) models. These include maximum likelihood (ML), expected a priori (EAP), modal a priori (MAP), and weighted maximum likelihood (WML) estimators, as well as the most commonly used approach based on translating ratings through the test characteristic curve (i.e., the IRT true‐score (TS) estimator). The five methods are compared using a simulation study and a real data example. Results indicated that the application of different methods can sometimes lead to different estimated cut scores, and that there can be some key differences in impact data when using the IRT TS estimator compared to other methods. It is suggested that one should carefully think about their choice of methods to estimate ability and cut scores because different methods have distinct features and properties. An important consideration in the application of Bayesian methods relates to the choice of the prior and the potential bias that priors may introduce into estimates.