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聚类数据的扩展广义估计方程AI 解读

Typically, analysis of data consisting of multiple observations on a cluster is complicated by within-cluster correlation. Estimating equations for generalized linear modeling of clustered data have recently received much attention. This article proposes an extension to the generalized estimating equation method proposed by Liang and Zeger, which treats within-cluster correlations as nuisance parameters. Using ideas from extended quasi-likelihood, estimating equations for…

为估计共同成功概率而序贯选择两类实验AI 解读

To estimate a success probability p, two experiments are available: individual Bernoulli (p) trials or the product of τ individual Bernoulli (p) trials. This problem has its roots in reliability where either single components can be tested or a system of τ identical components can be tested. A total of N experiments can be performed, and the problem is to sequentially select some combination (allocation) of these two experiments, along with an estimator of p, to achieve low…

单元格含多个计数的双因素计数数据分析AI 解读

Multiple counts may occur in each cell of an a × b two-way layout (balanced or unbalanced) of two fixed factors A and B. Standard log-linear model analysis based on a Poisson distribution assumption of the cell counts is not applicable here, because of the unbalanced nature of the table or because the Poisson distribution assumption is not valid. We develop C(α) tests for interaction and main effects assuming data to be Poisson distributed and also assuming that data within…

连接函数与方差函数未知时的拟似然回归AI 解读

We consider the multiple regression model E(y) = μ, μ = g(x T β), var(y) — [sgrave]2(μ) with predictors x, link function g, and variance function [sgrave]2(·). The aim is to reduce the assumptions in a fully parametric generalized linear model or a quasi-likelihood model by allowing the link and the variance functions to be unknown but smooth. These functions are then estimated nonparametrically, and the estimates are substituted into the quasi-likelihood function. We…

多个二乘二表共同优势比的近似精确推断AI 解读

The conditional maximum likelihood estimator (MLE) of the common odds ratio in a sequence of independent 2 × 2 tables is known to be superior to the Mantel–Haenszel estimator in terms of asymptotic efficiency and has the further advantage that its exact distribution is known. However, a long-standing barrier to the widespread use of this estimator has been computational intractability; in particular, the calculation of significance levels, confidence sets, and power based on…

为估计共同成功概率而序贯选择两类实验AI 解读

To estimate a success probability p, two experiments are available: individual Bernoulli (p) trials or the product of τ individual Bernoulli (p) trials. This problem has its roots in reliability where either single components can be tested or a system of τ identical components can be tested. A total of N experiments can be performed, and the problem is to sequentially select some combination (allocation) of these two experiments, along with an estimator of p, to achieve low…

每格含多个计数的双因素布局分析AI 解读

Multiple counts may occur in each cell of an a × b two-way layout (balanced or unbalanced) of two fixed factors A and B. Standard log-linear model analysis based on a Poisson distribution assumption of the cell counts is not applicable here, because of the unbalanced nature of the table or because the Poisson distribution assumption is not valid. We develop C(α) tests for interaction and main effects assuming data to be Poisson distributed and also assuming that data within…

链接函数与方差函数未知的拟似然回归AI 解读

We consider the multiple regression model E(y) = μ, μ = g(x T β), var(y) — [sgrave]2(μ) with predictors x, link function g, and variance function [sgrave]2(·). The aim is to reduce the assumptions in a fully parametric generalized linear model or a quasi-likelihood model by allowing the link and the variance functions to be unknown but smooth. These functions are then estimated nonparametrically, and the estimates are substituted into the quasi-likelihood function. We…

聚类数据的扩展广义估计方程AI 解读

Typically, analysis of data consisting of multiple observations on a cluster is complicated by within-cluster correlation. Estimating equations for generalized linear modeling of clustered data have recently received much attention. This article proposes an extension to the generalized estimating equation method proposed by Liang and Zeger, which treats within-cluster correlations as nuisance parameters. Using ideas from extended quasi-likelihood, estimating equations for…

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一类局部似然方法与近参数渐近理论AI 解读

Summary The local maximum likelihood estimate θ^ t of a parameter in a statistical model f(x, θ) is defined by maximizing a weighted version of the likelihood function which gives more weight to observations in the neighbourhood of t. The paper studies the sense in which f(t, θ^t) is closer to the true distribution g(t) than the usual estimate f(t, θ^) is. Asymptotic results are presented for the case in which the model misspecification becomes vanishingly small as the…

弱工具变量回归中结构参数的推断AI 解读

The authors consider the problem of making asymptotically valid inference on structural parameters in instrumental variables regression with weak instruments. Using local-to-zero asymptotics, they derive the asymptotic distributions of likelihood ratio (LR) and Lagrange multiplier (LM) type statistics for testing simple hypotheses on structural parameters based on maximum likelihood and generalized methods of moments estimation methods. In contrast to the nonstandard…

风险率模型复合假设的平滑拟合优度检验AI 解读

Consider a counting process $N(t), t\inT}$ with compensator process ${A(t),t\in T}$, where $A(t)=\int_0^t Y(s) ds, {Y(t), t\in T}$ is an observable predictable process, and $\lambda_0(\dot)$ is an unknown hazard rate function. A general procedure for extending Neyman’s smooth goodness­of­fit test for the composite null hypothesis $H_0: \lambda_0(\dot)\inC ={\lambda_0(\dot;\eta):\eta\in\Gamma\subseteq\Re^q}$ is proposed and developed. The extension is obtained by embedding $C$…

单元概率受凸约束的对数凸模型：通过对偶求极大似然估计AI 解读

The purpose of this article is to derive and illustrate a method for fitting models involving both convex and log-convex constraints on the probability vector(s) of a (product) multinomial distribution. We give a two-step algorithm to obtain maximum likelihood estimates of the probability vector(s) and show that it is guaranteed to converge to the true solution. Some examples are discussed which illustrate the procedure.

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存在干扰参数时用于推断的似然函数AI 解读

Consider inference about a scalar parameter of interest Θ in the presence of a vector nuisance parameter. Inference about Θ is often based on a pseudolikelihood function. In this paper, the general problem of constructing a pseudo-loglikelihood function H(Θ) is considered. Conditions are given under which H has the same properties as a genuine loglikelihood function for a model without a nuisance parameter. When these conditions are satisfied to a given order of…

Isserlis 矩阵及其在不可分解高斯图模型中的应用AI 解读

The operations of matrix completion and Isserlis matrix construction arise in the statistical analysis of graphical Gaussian models, in both the Bayesian and frequentist approaches. In this paper we study the properties of the Isserlis matrix of the completion, , of a positive definite matrix and propose an edge set indexing notation which highlights the symmetry existing between and its Isserlis matrix. In this way well-known properties of can be exploited to give an easy…

通过最小化密度幂散度实现稳健高效估计AI 解读

A minimum divergence estimation method is developed for robust parameter estimation. The proposed approach uses new density-based divergences which, unlike existing methods of this type such as minimum Hellinger distance estimation, avoid the use of nonparametric density estimation and associated complications such as bandwidth selection. The proposed class of ‘density power divergences’ is indexed by a single parameter α which controls the trade-off between robustness and…

局部最大似然估计与推断AI 解读

Summary Local maximum likelihood estimation is a nonparametric counterpart of the widely used parametric maximum likelihood technique. It extends the scope of the parametric maximum likelihood method to a much wider class of parametric spaces. Associated with this nonparametric estimation scheme is the issue of bandwidth selection and bias and variance assessment. This paper provides a unified approach to selecting a bandwidth and constructing confidence intervals in local…

混合效应模型的快速EM类算法实现AI 解读

Summary The mixed effects model, in its various forms, is a common model in applied statistics. A useful strategy for fitting this model implements EM-type algorithms by treating the random effects as missing data. Such implementations, however, can be painfully slow when the variances of the random effects are small relative to the residual variance. In this paper, we apply the ‘working parameter’ approach to derive alternative EM-type implementations for fitting mixed…

二元空间数据的复合似然方法AI 解读

Conventional geostatistics addresses the problem of estimation and prediction for continuous observations. But in many practical applications in public health, environmental remediation, or ecological research the most commonly available data are in the form of counts (e.g., number of cases) or indicator variables denoting above or below threshold values. Also, in many situations it is less expensive to obtain an imprecise categorical observation than to obtain precise…

两种参数化多项超额变异模型的大簇结果AI 解读

Two parametric extra variation models are considered. Approximate closed-form expressions are given for the Fisher information matrices. The expressions are useful in computing maximum likelihood estimates and obtaining large cluster efficiencies. A simulation study shows that the approximations perform very well even in clusters of moderate size. The models are applied in illustrative examples. A goodness-of-fit test is developed that is applicable even when the cluster…

嵌套与交叉曲线样本分析的平滑样条模型AI 解读

We introduce a class of models for an additive decomposition of groups of curves stratified by crossed and nested factors, generalizing smoothing splines to such samples by associating them with a corresponding mixed-effects model. The models are also useful for imputation of missing data and exploratory analysis of variance. We prove that the best linear unbiased predictors (BLUPs) from the extended mixed-effects model correspond to solutions of a generalized penalized…