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作为 Cox 模型诊断工具的鞅差残差AI 解读

The proportional hazards model makes two major assumptions: the hazard ratio is constant over time, and the relationship between the hazard and continuous covariates is log‐linear. Methods exist for checking and relaxing each of these assumptions, but in both cases the methods rely on the other assumption being true. Problems can occur if neither of the assumptions is appropriate, or even if only one of the assumptions is appropriate but it is not known which. We propose a…

一类非参数似然检验的二阶功效比较AI 解读

This paper compares the second‐order power properties of a broad class of nonparametric likelihood tests recently introduced by Baggerly (1998) as a generalisation of Owen's (1988) empirical likelihood. It is shown that in a multi‐parameter setting identity of power up to first order does not imply identity up to second order unless one considers the average power criterion. It is also shown that the empirical likelihood ratio enjoys an optimality property in terms of local…

纵向数据大规模协方差矩阵的非参数估计AI 解读

Estimation of an unstructured covariance matrix is difficult because of its positive‐definiteness constraint. This obstacle is removed by regressing each variable on its predecessors, so that estimation of a covariance matrix is shown to be equivalent to that of estimating a sequence of varying‐coefficient and varying‐order regression models. Our framework is similar to the use of increasing‐order autoregressive models in approximating the covariance matrix or the spectrum…

协方差选择模型的高效估计AI 解读

A Bayesian method is proposed for estimating an inverse covariance matrix from Gaussian data. The method is based on a prior that allows the off‐diagonal elements of the inverse covariance matrix to be zero, and in many applications results in a parsimonious parameterisation of the covariance matrix. No assumption is made about the structure of the corresponding graphical model, so the method applies to both nondecomposable and decomposable graphs. All the parameters are…

Poisson计数的观测驱动模型AI 解读

This paper is concerned with a general class of observation‐driven models for time series of counts whose conditional distributions given past observations and explanatory variables follow a Poisson distribution. These models provide a flexible framework for modelling a wide range of dependence structures. Conditions for stationarity and ergodicity of these processes are established from which the large‐sample properties of the maximum likelihood estimators can be derived.…

用桥接分布匹配二元随机截距模型的条件与边际函数形式AI 解读

SUMMARY Random effects logistic regression models are often used to model clustered binary response data. Regression parameters in these models have a conditional, subject-specific interpretation in that they quantify regression effects for each cluster. Very often, the logistic functional shape conditional on the random effects does not carry over to the marginal scale. Thus, parameters in these models usually do not have an explicit marginal, population-averaged…

不可忽略无应答下的多元缺失数据分析AI 解读

We consider multivariate regression analysis with missing data in the outcome variables, when the nonresponse mechanism depends on the underlying values of the responses and hence is nonignorable. Related problems include response‐biased sampling where data are sampled with probability depending only on the univariate response. Our methods do not require specification of the form of the nonresponse mechanism. We show that, under certain regularity conditions, all the…

概率与统计史研究第四十八篇：Ernest Lhoste 的贝叶斯贡献AI 解读

The contributions of Ernest Lhoste are largely unknown outside France, and even within that country are not well known. His important contributions were in the two areas of the development of prior distributions that represent little or no information, and a sophisticated posterior analysis for normal and binomial populations. His results are similar to those of Haldane (1948) and Jeffreys (1961), but they appeared much earlier, in 1923. He gave a great deal of thought to…

加速失效时间模型下的个体生存函数估计AI 解读

We use the semiparametric accelerated failure time model to predict the survival function and its related quantities for future subjects with a given set of covariates. We derive the large‐sample distribution for the subject‐specific cumulative hazard function estimate. We then propose a simple resampling technique for constructing pointwise confidence intervals and simultaneous bands for the corresponding survival function and its quantile function over a properly selected…

相关矩阵的主成分模型AI 解读

Distributional theory regarding principal components is less well developed for correlation matrices than it is for covariance matrices. The intent of this paper is to reduce this disparity. Methods are proposed that enable investigators to fit and to make inferences about flexible principal components models for correlation matrices. The models allow arbitrary eigenvalue multiplicities and allow the distinct eigenvalues to be modelled parametrically or nonparametrically.…

球面回归AI 解读

Methods are introduced for regressing points on the surface of one sphere on points on another. Complex variables and stereographic projection are used to deal with theoretical problems of directional statistics much as they have been used historically to deal with problems in non‐Euclidean geometry. The complex plane harbours the group of Möbius transformations, and stereographic projection is used as a bridge to map these Möbius transforms to regression link functions on…

Cox 部分似然的贝叶斯论证AI 解读

In this paper, we establish both naive and formal Bayesian justifications of Cox's (1975) partial likelihood and its various modifications. We extend the original work of Kalbfieisch (1978), who showed that the partial likelihood is a limiting marginal posterior under noninformative priors for baseline hazards. We extend the result to scenarios with time‐dependent covariates and time‐varying regression parameters. We establish results for continuous time as well as grouped…

含扩散与离散分量的马尔可夫过程的贝叶斯推断AI 解读

Data arising in certain radio‐tracking experiments consist of both a continuous spatial component and a discrete component related to behaviour. This leads naturally to stochastic models with a state space which is a product of continuous and discrete components. We consider a class of such models in continuous time, which can be thought of as diffusions in random environments. They are related to switching diffusion or hidden Markov models, but observations are made on both…

序贯试验停止后次级过程的推断AI 解读

We consider the following sequential testing problem. A group‐sequential or fully‐sequential test is carried out for a primary parameter, using a score process or an effective score process to eliminate nuisance parameters. After stopping, the possibility of additional parameters is considered, and appropriate tests and estimators are desired that recognise the sequential stopping rule. We formulate an asymptotic multi‐dimensional Gaussian process form of such problems, and…

利用逻辑回归程序估计 ROC 曲线AI 解读

Estimation of a receiver operating characteristic, ROC, curve is usually based either on a fully parametric model such as a normal model or on a fully nonparametric model. In this paper, we explore a semiparametric approach by assuming a density ratio model for disease and disease‐free densities. This model has a natural connection with the logistic regression model. The proposed semiparametric approach is more robust than a fully parametric approach and is more efficient…

测量误差模型的几何结构AI 解读

The problem of undertaking inference in the classical linear model when the covariates have been measured with error is investigated from a geometric point of view. Under the assumption that the measurement error is small, relative to the total variation in the data, a new model is proposed which has good inferential properties. An inference technique which exploits the geometric structure is shown to be computationally simple, efficient and robust to measurement error. The…

广义结构化模型AI 解读

We present a general class of nonlinear regression and time series models that we call generalised structured models. The class is a natural generalisation of generalised additive models, and it includes generalised interaction models, structured volatility models, visual GARCH, generalised autoregressive conditional heteroscedasticity, models and varying coefficient models. We discuss estimation principles including smoothing splines and a generalisation of the projection…

含分层干扰参数模型的修正剖面似然AI 解读

It is well known, at least through many examples, that when there are many nuisance parameters modified profile likelihoods often perform much better than the profile likelihood. Ordinary asymptotics almost totally fail to deal with this issue. For this reason, we study asymptotic properties of the profile and modified profile likelihoods in models for stratified data in a two‐index asymptotics setting. This means that both the sample size of the strata, m, and the dimension…

通过条件化降低一般估计函数对干扰参数的敏感性AI 解读

A conditional method is presented that renders an estimating function insensitive to nuisance parameters. The approach is a generalisation of the conditional score method to a general estimating function context and does not require complete specification of the probability model. We exploit the informal relationship between general estimating functions and score functions to derive simple generalisations of sufficient and partially ancillary statistics, referred to as…

因果推断中的一致一致性AI 解读

There is a long tradition of representing causal relationships by directed acyclic graphs (Wright, 1934). Spirtes (1994), Spirtes et al. (1993) and Pearl & Verma (1991) describe procedures for inferring the presence or absence of causal arrows in the graph even if there might be unobserved confounding variables, and/or an unknown time order, and that under weak conditions, for certain combinations of directed acyclic graphs and probability distributions, are asymptotically,…

个体匹配病例—对照数据中发生率比估计的稳健方差AI 解读

The asymptotic variance and robust variance estimators of rate ratios estimated using conditional logistic regression from individually‐matched case‐control data are derived when the presumed proportional hazards model is misspecified. The robust variance estimators are easily computed using Schoenfeld residuals generated from standard partial likelihood estimation software for failure time data. Simulation studies indicate that the robust variance estimators perform well…

重复测量数据的秩回归AI 解读

A rank‐based regression method is proposed for repeated measurements data. It is a generalisation of the classical Wilcoxon–Mann–Whitney rank statistic for independent observations. The method is valid under a weak condition on the error terms that can accommodate certain heteroscedasticity and within‐subject dependency. The asymptotic normality of the proposed estimator is proved using empirical process theory. A variance estimator, shown to be consistent, is also…

可识别性与删失数据AI 解读

It is well known that, without the assumption of independence between two nonnegative random variables X and Y, the survival function of X is not identifiable on the basis of the joint distribution function of Z = min(X, Y) and δ = I(Z = Y). In this paper, we provide a simple condition in the form of conditional distribution of Y given X. We show that our condition is equivalent to the constant‐sum condition proposed by Williams & Lagakos (1977). As a result the survival…

异方差门限自回归模型的门限小波检验与估计AI 解读

We consider the testing and estimation of thresholds in heteroscedastic threshold autoregressive models with an unknown number of thresholds. A test statistic based on empirical wavelet coefficients is proposed. The asymptotic distribution of the test statistic is established and consistent estimators of the thresholds and the number of thresholds are given. A Monte Carlo study and a real example are used to assess the performance of our method.