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协方差结构对平衡随机参数增长曲线模型方差估计的影响AI 解读

Intuition suggests that altering the covariance structure of a parametric model for repeated-measures data alters the variances of the model's estimated mean parameters. The purpose of this article is to sharpen such intuition for a family of growth-curve models with differing numbers of random effects for the individual sampling units and with a fixed structure on the mean. For every member of this family, the maximum likelihood (ML) estimator of the fixed effects is…

协变量部分缺失时删失生存数据的对数线性分析AI 解读

Log-linear models provide a flexible means of extending life table techniques for the analysis of censored survival data with categorical covariates, as discussed by Holford (1980) and Laird and Olivier (1981). We extend this methodology to incorporate cases in which one or more of the categorical covariates are sometimes missing. Maximum likelihood estimates of the parameters are calculated using data from all cases. This can result in large gains in efficiency over…

缺失数据的统计分析AI 解读

Preface.PART I: OVERVIEW AND BASIC APPROACHES.Introduction.Missing Data in Experiments.Complete-Case and Available-Case Analysis, Including Weighting Methods.Single Imputation Methods.Estimation of Imputation Uncertainty.PART II: LIKELIHOOD-BASED APPROACHES TO THE ANALYSIS OF MISSING DATA.Theory of Inference Based on the Likelihood Function.Methods Based on Factoring the Likelihood, Ignoring the Missing-Data Mechanism.Maximum Likelihood for General Patterns of Missing Data:…

非平稳时间序列与经济周期分析的新方法AI 解读

This paper models occasional, discrete shifts in the growth rate of a nonstationary series. Algorithms for inferring these unobserved shifts are presented, a byproduct of which permits estimation of parameters by maximum likelihood. An empirical application of this technique suggests that the periodic shift from a positive growth rate to a negative growth rate is a recurrent feature of the U.S. business cycle, and indeed could be used as an objective criterion for defining…

特征函数估计的切比雪夫多项式近似：若干理论补充AI 解读

SUMMARY Densities for the angle Θ = uX(mod 2π) and the cosine Y = cos(uX) can be expressed, through Fourier methods, in terms of the characteristic function of X. Thus, if X has a characteristic function of closed form, the parameters of its distribution may be estimated by maximum likelihood. The paper addresses the problems of estimability of asymmetric distributions and situations where the method may not apply.

嵌套 Logit 模型的有效估计AI 解读

This article examines the sequential, full information maximum likelihood (FIML), and linearized maximum likelihood (LML) estimators for a nested logit model of time-of-day choice for work trips. These estimators are compared using a Monte Carlo study based on specification and data from a previously published empirical study. The sequential estimator is found to be much less efficient than LML or FIML, and its uncorrected second-stage standard-error estimates are strongly…

凸到达率的最大似然估计AI 解读

It is commonly believed that failures of a repairable system follow a time dependent Poisson process with ‘bathtub-shaped’ arrival rate. A natural problem then is maximum likelihood estimation of arrival rate subject to the constraint that it be convex. This paper employs theoretical considerations to reduce that task to a finite dimensional nonlinear programming problem and completes the solution by computer. The resulting estimates are interesting graphical presentations…

混合图交互模型中最大似然估计的分解AI 解读

We show how decompositions of marked graphs induce corresponding decompositions of maximum likelihood estimates in mixed graphical interaction models. We use this result to obtain explicit formulae for the estimates in decomposable models and to obtain factorizations of likelihood ratio statistics.

It is shown that the iterative least-squares procedure for estimating the parameters in a general multilevel random coefficients linear model can be modified to produce unbiased estimates of the random parameters. In the multivariate normal case these are equivalent to restricted maximum likelihood estimates.

剖面似然的调整AI 解读

Conditional and marginal likelihoods constructed from parameter-dependent functions of the data have an additional parameter dependence that changes with the choice of supporting metric for the corresponding densities. We consider constructing marginal and conditional likelihoods by using densities expressed in terms of an instrinsic choice of support measure, based on either Euclidean metric or the constant information metric. Barndorff-Nielsen's (1983) approximation to the…

啮齿动物生物测定与筛查实验中协变量的使用AI 解读

Equation (6) represents only an approximation to the maximum likelihood estimator, whose actual form satisfies where Our reason for presenting (6) is its generalizability to the closed form, consistent prevalence estimator, (8).

混合模型的似然推断：单调步长算法的几何及其他构造AI 解读

This paper considers algorithms for the maximum likelihood estimator of the mixing distribution of a family of parametric densities. Specific interest is devoted to the monotonicity of the step-length of the solution. In ξ 2 we introduce the idea of estimating the area above the second derivative curve, and in Theorem 1 we relate area-overestimation to the monotonicity of the associated algorithm. In ξ 3 we apply Theorem 1 to the monotonicity analysis of well-known…

一般随机序约束下生存函数的非参数最大似然估计及其对偶AI 解读

This paper discusses estimation of survival functions under an arbitrary partial stochastic ordering of the underlying populations. This technique is especially useful when data are not easily acquired from one or more of the populations, but data from the other populations are available. Estimation of the ordered survival functions entails use of a Fenchel duality theorem that results in an algorithm to identify and resolve violations of the underlying ordering. The…

自相关误差回归模型的大样本推断AI 解读

SUMMARY Based on intermittent observations from several independent regression models with autocorrelated errors, we derive tests of homogeneity, and the maximum likelihood estimate of the common regression parameter. The estimate for the regression parameter is based on aggregated data in the form of sample means at each time point. The limit distributions of the test statistics, and the estimate are considered. Basawa, Billard & Srinivasan (1984) discussed testing the…

形状数据的统计分析AI 解读

The paper deals with the statistical shape analysis of landmark data. Bookstein (1986) introduced a plausible model and obtained a useful normal approximation for three landmarks. We use exact distribution theory and a normal approximation to consider maximum likelihood estimation. The Fisher information matrix for the normal approximation is given and we consider the hypothesis of shape change. Using these results, we analyse a practical example based on digitized shapes.…

两个变量均有测量误差时简单线性回归的似然估计AI 解读

Likelihood based methods for obtaining approximate confidence intervals for the slope in a simple linear regression when both variables are measured with error are discussed and compared. We also derive a Bartlett correction factor for the likelihood ratio statistic. The improvement of the chi-squared approximation is appreciable in the unknown variance case. Further, the distribution of the maximum likelihood slope estimator is obtained from the joint distribution of sample…

一类半参数模型中实值参数的估计AI 解读

We study semiparametric models where for a fixed value of the finite-dimensional parameter there exists a sufficient statistic for the nuisance parameter. An asymptotically normal sequence of estimators for the parametric component is constructed, which is efficient under the assumption that projecting on the set of nuisance scores is equivalent to taking conditional expectations given the sufficient statistic. The latter property is checked for a number of examples, in…

利用局部影响进行回归变换诊断AI 解读

Following Box and Cox (1964), the use of transformations in regression analysis is now common; recently there has been emphasis on diagnostic methods for transformation, much of which has involved deletion of data cases. Summaries were given by Cook and Weisberg (1982) and Atkinson (1985). This article obtains diagnostics for the estimated regression parameter of the Box-Cox transformation of the response variable in the linear model. Instead of deleting cases, the more…

协变量测量误差回归的近似修正AI 解读

The effect of covariate measurement error on maximum likelihood and maximum quasilikelihood estimates (MLE's or MQLE's) of regression parameters is considered. The naive estimates, obtained by ignoring error, are modified to account for it. The modified estimates can be computed explicitly from the naive ones, and have less bias for small error. They are particularly useful for Berkson error models. Examples illustrate their application to linear and nonlinear regression,…

重复测量线性混合效应模型的 Newton–Raphson 与 EM 算法AI 解读

We develop an efficient and effective implementation of the Newton—Raphson (NR) algorithm for estimating the parameters in mixed-effects models for repeated-measures data. We formulate the derivatives for both maximum likelihood and restricted maximum likelihood estimation and propose improvements to the algorithm discussed by Jennrich and Schlüchter (1986) to speed convergence and ensure a positive-definite covariance matrix for the random effects at each iteration. We use…

非线性指数族回归模型的极大似然与拟似然AI 解读

Linear and nonlinear exponential family and quasi-likelihood regression models form a class of models with a structure that invites using one algorithmic framework to compute parameter estimates and regression diagnostics. This framework extends our work on nonlinear least squares; it includes iteratively reweighted least squares but also encompasses secant updates for part of the Hessian matrix of the likelihood or quasi-likelihood function along with tests for when to use…

类间相关系数的估计AI 解读

A noniterative method for estimating the interclass correlation coefficient is derived from the technique of weighted sums of squares. The asymptotic variance of this estimator is derived under the assumption of normality. Through extensive Monte Carlo simulations, the sample variance of this estimator is found not to differ greatly from that of the maximum likelihood estimator.

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