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受试者工作特征曲线的非参数置信区间AI 解读

We study methods for constructing confidence intervals and confidence bands for estimators of receiver operating characteristics. Particular emphasis is placed on the way in which smoothing should be implemented, when estimating either the characteristic itself or its variance. We show that substantial undersmoothing is necessary if coverage properties are not to be impaired. A theoretical analysis of the problem suggests an empirical, plug‐in rule for bandwidth choice,…

测量可交换性与正态单因子模型AI 解读

The one‐factor model restricts the covariance structure of the observed variables on the basis of assumptions about their relationship with an unobserved variable. It is hard to justify these assumptions on substantive or empirical grounds. In this paper, alternative measurement models are proposed that are based on exchangeability of variables after admissible scale transformations. They provide an alternative interpretation of the model and do not involve unobserved…

Higher‐order approximations to the distribution of the likelihood ratio statistic are considered for a class of nonregular models in which the maximum likelihood estimator of the parameter of interest is asymptotically distributed according to an exponential, rather than a normal, distribution. Asymptotic behaviour of this type often arises when the boundary of the support of the distributions under consideration depends on θ. A modified likelihood ratio statistic is…

贝叶斯小波估计中的后验概率区间AI 解读

We use saddlepoint approximation to derive credible intervals for Bayesian wavelet regression estimates. Simulations show that the resulting intervals perform better than the best existing method.

相关回归误差的非参数检测AI 解读

In regression problems it is hard to detect correlated errors since the errors are not observed. In this paper, a nonparametric method is proposed for the detection of correlated errors when the design points are equally spaced. It turns out that the first‐order sample autocovariance of the residuals from the kernel regression estimates provides essential information about correlated errors and its bootstrap is quite effective in implementing such information.

适用于二元数据的高效 Robbins–Monro 程序AI 解读

The Robbins–Monro procedure does not perform well in the estimation of extreme quantiles, because the procedure is implemented using asymptotic results, which are not suitable for binary data. Here we propose a modification of the Robbins–Monro procedure and derive the optimal procedure for binary data under some reasonable approximations. The improvement obtained by using the optimal procedure for the estimation of extreme quantiles is substantial.

贝叶斯线性运动学与贝叶斯线性—贝叶斯图模型AI 解读

Probability kinematics (Jeffrey, 1965, 1983) furnishes a method for revising a prior probability specification based upon new probabilities over a partition. We develop a corresponding Bayes linear kinematic for a Bayes linear analysis given information which changes our beliefs about a random vector in some generalised way. We derive necessary and sufficient conditions for commutativity of successive Bayes linear kinematics which depend upon the eigenstructure of the joint…

含测量误差回归中的主 Hessian 方向AI 解读

We consider a nonlinear regression problem with predictors with measurement error. We assume that the response is related to unknown linear combinations of a p‐dimensional predictor vector through an unknown link function. Instead of observing the predictors, we observe a surrogate vector with the property that its expectation is linearly related to the predictor vector with constant variance. We use an important linear transformation of the surrogates. Based on the…

利用小规模暴发估计疫苗效力AI 解读

Let CV and C0 denote the number of cases among vaccinated and unvaccinated individuals, respectively, and let υ be the proportion of individuals vaccinated. The quantity ê = 1–(1–υ)CV/(υC0) = 1–(relative attack rate) is the most used estimator of the effectiveness of a vaccine to protect against infection. For a wide class of vaccine responses, a family of transmission models and three types of community settings, this paper investigates what ê actually estimates. It does so…

家庭群体中随机多类型流行病的阈值参数与安全接种覆盖率估计AI 解读

This paper is concerned with estimation of the threshold parameter R* for a stochastic model for the spread of a susceptible → infective → removed epidemic among a closed, finite population that contains several types of individual and is partitioned into households. It turns out that R* cannot be estimated consistently from final outcome data, so a Perron–Frobenius argument is used to obtain sharp lower and upper bounds for R*, which can be estimated consistently.…

半参数变换治愈模型AI 解读

A general class of semiparametric transformation cure models is studied for the analysis of survival data with long‐term survivors. It combines a logistic regression for the probability of event occurrence with the class of transformation models for the time of occurrence. Included as special cases are the proportional hazards cure model (Farewell, 1982; Kuk & Chen, 1992; Sy & Taylor, 2000; Peng & Dear, 2000) and the proportional odds cure model. Generalised estimating…

病例对照研究中的纵向数据分析AI 解读

Case‐control studies for longitudinal data are considered. Among repeated binary measurements of disease status in each subject, the exposure levels of risk factors for all diseased cases are identified and the exposure levels for only a small fraction of disease‐free cases, to be regarded as controls, are identified. Case‐control studies for longitudinal data bring about economies in cost and time when the disease is rare and when assessing the exposure level of risk…

病例队列删失数据半参数变换模型的加权估计方程AI 解读

SUMMARY In a case-cohort design introduced by Prentice (1986), covariates are assembled only for a subcohort randomly selected from the entire cohort, and any additional cases outside the subcohort. Semiparametric transformation models are considered here for failure time data from the case-cohort design. Weighted estimating equations are proposed for esti mation of the regression parameters. The estimation procedure of survival probability at given covariate levels is also…

双重删失数据的半参数回归分析AI 解读

We analyse doubly censored data using semiparametric transformation models. We provide inference procedures for the regression parameters and derive the asymptotic distributions of the proposed estimators. Procedures for model checking and model selection are also discussed. We illustrate our approach with a viral‐load dataset from a recent AIDS clinical trial.

基于加权对数秩统计量的聚类生存数据样本量公式AI 解读

We present a simple sample‐size formula for weighted log‐rank statistics applied to clustered survival data with variable cluster sizes and arbitrary treatment assignments within clusters. This formula is based on the asymptotic normality of weighted log‐rank statistics under certain local alternatives in the clustered data context. We also provide consistent variance estimators. The derived sample‐size formula reduces to Schoenfeld's (1983) formula for cases of no…

中等偏差事件的高效重要性抽样及其应用AI 解读

We propose a method for finding the alternative distribution in importance sampling. The alternative distribution is optimal in the sense that the asymptotic variance is minimised for estimating tail probabilities of asymptotically normal statistics. Our contribution to importance sampling is three‐fold. To begin with, we obtain an explicit expression for the mean of the optimal alternative distribution and the expression motivates a recursive approximation algorithm.…

广义估计方程与二次推断函数的稳健性评估AI 解读

In the presence of data contamination or outliers, some empirical studies have indicated that the two methods of generalised estimating equations and quadratic inference functions appear to have rather different robustness behaviour. This paper presents a theoretical investigation from the perspective of the influence function to identify the causes for the difference. We show that quadratic inference functions lead to bounded influence functions and the corresponding…

随机线性假设的非参数推断及高维应用AI 解读

The Mann–Whitney–Wilcoxon rank sum test is limited to comparison of two groups with univariate responses. In this paper, we introduce a class of stochastic linear hypotheses that addresses these limitations within a nonparametric setting. We formulate hypotheses for simultaneous comparisons of several, multivariate response groups, without modelling the response distributions. Inference is developed based on U‐statistics theory and an exchangeability assumption. The latter…

双变量似不相关回归模型的似然多峰性AI 解读

We analyse the simplest two‐equation seemingly unrelated regressions model and demonstrate that its likelihood may have up to five stationary points, and thus there may be up to three local modes. Consequently the estimates obtained via iterative estimation methods may depend on starting values. We further show that the probability of multimodality vanishes asymptotically. Monte Carlo simulations suggest that multimodality rarely occurs if the seemingly unrelated regressions…

顺序多元失效时间数据的间隔时间风险回归AI 解读

Sequentially ordered multivariate failure time data are often observed in biomedical studies and inter‐event, or gap, times are often of interest. Generally, standard hazard regression methods cannot be applied to the gap times because of identifiability issues and induced dependent censoring. We propose estimating equations for fitting proportional hazards regression models to the gap times. Model parameters are shown to be consistent and asymptotically normal. Simulation…

We study the profile‐kernel and backfitting methods in partially linear models for clustered/longitudinal data. For independent data, despite the potential root‐n inconsistency of the backfitting estimator noted by Rice (1986), the two estimators have the same asymptotic variance matrix, as shown by Opsomer & Ruppert (1999). In this paper, theoretical comparisons of the two estimators for multivariate responses are investigated. We show that, for correlated data, backfitting…

基于自然指数族二次方差函数模型与调查权重的小区域估计AI 解读

We propose pseudo empirical best linear unbiased estimators of small‐area means based on natural exponential family quadratic variance function models when the basic data consist of survey‐weighted estimators of these means, area‐specific covariates and certain summary measures involving the weights. We also provide explicit approximate mean squared errors of these estimators in the spirit of Prasad & Rao (1990), and these estimators can be readily evaluated. A simulation…

利用渐近枢轴估计函数推断无限维参数AI 解读

Suppose that a consistent estimator for an infinite‐dimensional parameter can be readily obtained via a set of estimating functions which has a ‘good’ local linear approximation around the true value of the parameter. However, it may be difficult to estimate the variance function of this estimator well. We show that, if the set of estimating functions evaluated at the true parameter value is ‘asymptotically pivotal’, then the ‘fiducial’ distribution of the parameter can be…

分类数据的贝叶斯准则式模型评估AI 解读

We propose a general Bayesian criterion for model assessment for categorical data called the weighted L measure, which is constructed from the posterior predictive distribution of the data. The measure is based on weighting the observations according to the sampling variance of their future response vector. The weight component in the weighted L measure plays the role of a penalty term in the criterion, in which a greater weight assigned to covariate values implies a greater…