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边界约束下的条件复合似然比检验AI 解读

Composite likelihood has been widely used in applications. The asymptotic distribution of the composite likelihood ratio statistic at the boundary of the parameter space is a complicated mixture of weighted |$\chi^2$| distributions. In this paper we propose a conditional test with data-dependent degrees of freedom. We consider a modification of the composite likelihood which satisfies the second-order Bartlett identity. We show that the modified composite likelihood ratio…

协变量测量误差的局部辅助拟得分模型AI 解读

We use the notion of locally ancillary estimating functions to develop a quasi-score method for fitting regression models containing measurement error in the covariates. Suppose that interest is on the model E(Y|u, w) for response Y, the observed data are (y, x, w), and X is a mismeasured surrogate for u. We take a functional modeling approach, treating the u as a fixed nuisance parameter. Beginning with quasi-scores for the regression parameter and the unknown u, we derive…

非标准情形下的回归分析：成对伪似然方法AI 解读

Summary Regression analysis is one of the most used statistical methods for data analysis. There are, however, many situations in which one cannot base inference solely on f(y∣x; β), the conditional probability (density) function for the response variable Y, given x, the covariates. Examples include missing data where the missingness is non-ignorable, sampling surveys in which subjects are selected on the basis of the Y-values and meta-analysis where published studies are…

Summary When measurement error is present in covariates, it is well known that naïvely fitting a generalized linear model results in inconsistent inferences. Several methods have been proposed to adjust for measurement error without making undue distributional assumptions about the unobserved true covariates. Stefanski and Carroll focused on an unbiased estimating function rather than a likelihood approach. Their estimating function, known as the conditional score, exists…

伪似然比检验统计量的渐近行为AI 解读

SUMMARY This paper concerns the asymptotic distribution of the likelihood ratio statistic T for testing H 0: θ = θ 0 based on the pseudolikelihood L(θ,ϕ^), where ϕ^ is a simple estimator of ϕ. We show that the asymptotic distribution of T under H 0 is a weighted sum of independent χ 1 2-variables where the weights involve the asymptotic joint covariance matrix of ϕ^ and the score function for θ. Some sufficient conditions are provided for the limiting distribution to be χ 2.…

一般估计函数的近似似然比AI 解读

The method of estimating functions (Godambe, 1991) is commonly used when one desires to conduct inference about some parameters of interest but the full distribution of the observations is unknown. However, this approach may have limited utility, due to multiple roots for the estimating function, a poorly behaved Wald test, or lack of a goodness-of-fit test. This paper presents approximate likelihood ratios that can be used along with estimating functions when any of these…

一般估计函数的近似似然比AI 解读

The method of estimating functions (Godambe, 1991) is commonly used when one desires to conduct inference about some parameters of interest but the full distribution of the observations is unknown. However, this approach may have limited utility, due to multiple roots for the estimating function, a poorly behaved Wald test, or lack of a goodness-of-fit test. This paper presents approximate likelihood ratios that can be used along with estimating functions when any of these…

广义线性模型中的随机效应预测AI 解读

This article develops an estimating function-based approach to component estimation in the two-stage generalized linear model with univariate random effects and a vector of fixed effects. The novelty and unifying feature of the method is the use of estimating functions in the estimation of both the random effects and their variance. Two separate estimating procedures based on the method are proposed that differ in the intensity of numerical computation required. The…

分类数据的多元回归分析AI 解读

SUMMARY It is common to observe a vector of discrete and/or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes. The response vector can comprise repeated observations on one variable, as in longitudinal studies or genetic studies of families, or can include observations for different variables. This paper discusses a class of models…

大量干扰参数下的经验贝叶斯与条件推断AI 解读

This paper concerns the use of empirical Bayes methods to improve the efficiency of a parameter of interest, θ, in the presence of many nuisance parameters, {øi}, one from each data stratum. A class of distributions is introduced such that for fixed θ, the minimal sufficient statistic ti(θ) for øi is from an exponential family and hence complete. By imposing the assumption that the øi's are generated from an unspecified distribution function Q, we show that for this class of…

存在大量干扰参数时的经验贝叶斯与条件推断AI 解读

This paper concerns the use of empirical Bayes methods to improve the efficiency of a parameter of interest, θ, in the presence of many nuisance parameters, {øi}, one from each data stratum. A class of distributions is introduced such that for fixed θ, the minimal sufficient statistic ti(θ) for øi is from an exponential family and hence complete. By imposing the assumption that the øi's are generated from an unspecified distribution function Q, we show that for this class of…

通过估计函数扩展 Stein 估计程序AI 解读

This article extends the Stein method through the use of estimating functions (Godambe 1960) to address the simultaneous estimation of k population parameters, θ1, …, θ k , in a mixed model setting. The procedure generalizes the Stein method by (a) allowing us to deal effectively with complications, such as inequality of population variances, that may arise in non-Gaussian mixed models; (b) being appropriate for estimating θ i in populations of varying sizes and, in…

多元二元时间序列的一类 logistic 回归模型AI 解读

A logistic model for multivariate binary time series is proposed. First, we establish the equivalence between a log-linear model for the marginal distribution of a multivariate binary random vector and logistic models for the conditional distributions of each component given the others. The logistic formulation is used to describe a Markov chain for each series, which implies a Markov model for the vector of time series. A pseudolikelihood estimation procedure is presented.…

相关二元数据的条件Logistic回归模型AI 解读

A class of conditional logistic regression models for clustered binary data is considered. This includes the polychotomous logistic model of Rosner (1984) as a special case. Properties such as the joint distribution and pairwise odds ratio are investigated. A class of easily computed estimating functions is introduced which is shown to have high efficiency compared to the computationally intensive maximum likelihood approach. An example on chronic obstructive pulmonary…

相关二元数据的条件逻辑回归模型AI 解读

A class of conditional logistic regression models for clustered binary data is considered. This includes the polychotomous logistic model of Rosner (1984) as a special case. Properties such as the joint distribution and pairwise odds ratio are investigated. A class of easily computed estimating functions is introduced which is shown to have high efficiency compared to the computationally intensive maximum likelihood approach. An example on chronic obstructive pulmonary…

估计函数与近似条件似然AI 解读

The approximate conditional likelihood method proposed by Cox & Reid (1987) is applied to the estimation of a scalar parameter Θ, in the presence of nuisance parameters. The estimating function of Θ based on the approximate conditional likelihood is shown to be preferable to that based on the profile likelihood. A sufficient condition for both approaches to be equivalent is given. The role of parameter orthogonality is emphasized. Several examples including bivariate normal…

非标准条件下最大似然估计与似然比检验的渐近性质AI 解读

Large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described. Specifically, the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived. These results generalize the work of Moran (1971), Chant (1974), and Chernoff (1954). Some of Chant's results are shown to be incorrect. The approach used in deriving these results follows from comments made by Moran…

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估计函数与近似条件似然AI 解读

The approximate conditional likelihood method proposed by Cox & Reid (1987) is applied to the estimation of a scalar parameter Θ, in the presence of nuisance parameters. The estimating function of Θ based on the approximate conditional likelihood is shown to be preferable to that based on the profile likelihood. A sufficient condition for both approaches to be equivalent is given. The role of parameter orthogonality is emphasized. Several examples including bivariate normal…

多分层情形下同质性的局部最强检验AI 解读

A locally most powerful test is proposed for homogeneity of nuisance parameters from many strata in the mixed model setting. The test is based on the difference between the square of the score and the observed information about the nuisance parameters, all evaluated at the null hypothesis. Several examples including constant normal mean with possibly different variances and matched case-control studies are presented in detail. The relative efficiencies of the unstratified…

使用广义线性模型分析纵向数据AI 解读

This paper proposes an extension of generalized linear models to the analysis of longitudinal data. We introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence. The estimating equations are derived without specifying the joint distribution of a subject's observations yet they reduce to the score equations for niultivariate Gaussian outcomes. Asymptotic theory…

依赖数据下的优势比推断AI 解读

When data can be presented as a series of k 2×2 tables with cell counts (xi ,ni−xi, yi, mi−yi), it is often assumed that xi and yi are binomially distributed. This paper deals with inference for the common odds ratio Ψ when the binomial assumption is invalid. When k increases, the consistency and asymptotic normality of the Mantel & Haenszel (1959) estimator is derived. The conditional maximum likelihood estimator is shown to be inconsistent and the asymptotic bias is…

稀疏数据下优势比同质性的检验AI 解读

Three tests for homogeneity of odds ratio for a series of 2 × 2 tables when the data are sparse are studied by means of Monte Carlo experiments. A score test, based on the assumption that the log odds ratios are generated from some unknown distribution, is shown to be more powerful than the other two. The original test of Zelen (1971), later corrected by Halperin, Ware, Byar et al. (1977), is also examined. It tends to be too liberal under the sparse data situation; however,…

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