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利用聚合数据估计与插值马尔可夫链AI 解读

Given aggregated longitudinal data generated by a Markov chain, which may be nonhomogeneous, the problem considered is that of modelling, estimating and interpolating the logarithms of partial odds and hence the transition probabilities. By partial odds is meant the probability of a transition to another state divided by the probability of no transition. A result establishing asymptotic normality leads to vector weighted least squares estimation of parameterised partial odds…

失效原因缺失时检验生存分布治疗差异的多重插补方法AI 解读

We propose a method for comparing survival distributions when cause‐of‐failure information is missing for some individuals. We use multiple imputation to impute missing causes of failure, where the probability that a missing cause is that of interest may depend on auxiliary covariates, and combine log‐rank statistics computed from several ‘completed’ datasets into a test statistic that achieves asymptotically the nominal level. Simulations demonstrate the relevance of the…

利用经验似然获得调查回归估计中的范围受限权重AI 解读

Design weights in surveys are often adjusted to accommodate auxiliary information and to meet pre‐specified range restrictions, typically via some ad hoc algorithmic adjustment to a generalised regression estimator. In this paper, we present a simple solution to this problem using empirical likelihood methods or generalised regression. We first develop algorithms for computing empirical likelihood estimators and model‐calibrated empirical likelihood estimators. The first…

非平稳空间过程的谱方法AI 解读

We propose a nonstationary periodogram and various parametric approaches for estimating the spectral density of a nonstationary spatial process. We also study the asymptotic properties of the proposed estimators via shrinking asymptotics, assuming the distance between neighbouring observations tends to zero as the size of the observation region grows without bound. With this type of asymptotic model we can uniquely determine the spectral density, avoiding the aliasing…

极端依赖不确定性的模型与推断AI 解读

Conventionally, modelling of multivariate extremes has been based on the class of multivariate extreme value distributions. More recently, other classes have been developed, allowing for the possibility that, whilst dependence is observed at finite levels, the limit distribution is independent. A number of articles have shown this development to be important for accurate estimation of the extremal properties, both of theoretical processes and observed datasets. It has also…

随机函数分布结构的估计与展示AI 解读

We suggest a nonparametric approach to making inference about the structure of distributions in a potentially infinite‐dimensional space, for example a function space, and displaying information about that structure. It is suggested that the simplest way of presenting the structure is through modes and density ascent lines, the latter being the projections into the sample space of the curves of steepest ascent up the surface of a functional‐data density. Modes are always…

一类 logistic 型判别函数AI 解读

In two‐group discriminant analysis, the Neyman–Pearson Lemma establishes that the ROC, receiver operating characteristic, curve for an arbitrary linear function is everywhere below the ROC curve for the true likelihood ratio. The weighted area between these two curves can be used as a risk function for finding good discriminant functions. The weight function corresponds to the objective of the analysis, for example to minimise the expected cost of misclassification, or to…

半竞争风险数据分析AI 解读

SUMMARY We consider a variation of the competing risks problem in which a terminal event censors a non-terminal event, but not vice versa. The joint distribution of the events is formulated via a gamma frailty model in the upper wedge where data are observable (Day et al., 1997), with the marginal distributions unspecified. An estimator for the association parameter is obtained from a concordance estimating function. A novel plug-in estimator for the marginal distribution of…

模型误设的最大似然估计与广义线性混合模型AI 解读

We investigate the impact of model violations on the estimate of a regression coefficient in a generalised linear mixed model. Specifically, we evaluate the asymptotic relative bias that results from incorrect assumptions regarding the random effects. We compare the impact of model violation for two parameterisations of the regression model. Substantial bias in the conditionally specified regression point estimators can result from using a simple random intercepts model when…

依赖性右删失下生长曲线的两样本检验AI 解读

In many tumour growth inhibition studies, tumour sizes are recorded over a period of time, forming a growth curve for each experimental animal. A frequently asked question in these studies is whether or not different treatment agents/inhibitors result in different growth rates. To compare tumour growth rates under two treatments, either the t‐test or the Wilcoxon–Mann–Whitney test could be used under suitable assumptions, provided that a one‐dimensional variable, such as the…

家系研究中兼顾病例入选机制与随机遗传效应的协变量推断AI 解读

Family studies to identify disease‐related genes often collect families with multiple cases. If environmental exposures or other measured covariates are also important, they should be incorporated into these genetic analyses to control for confounding and increase statistical power. We propose a two‐level mixed effects model that allows us to estimate environmental effects while accounting for varying genetic correlations among family members and adjusting for ascertainment…

病例对照数据逻辑回归模型的信息矩阵检验AI 解读

We propose an information‐matrix‐based goodness‐of‐fit statistic to test the validity of the logistic regression model based on case‐control data by extending the information matrix test of White (1982) for detecting one‐sample parametric model misspecification to the semiparametric profile likelihood setting under a two‐sample semiparametric model, which is equivalent to the assumed logistic regression model. The proposed test statistic requires a high‐dimensional matrix…

摘要暂缺

Logistic 与 Poisson 回归模型的样本量计算AI 解读

A method is proposed for improving sample size calculations for logistic and Poisson regression models by incorporating the limiting value of the maximum likelihood estimates of nuisance parameters under the composite null hypothesis. The method modifies existing approaches of Whittemore (1981) and Signorini (1991) and provides explicit formulae for determining the sample size needed to test hypotheses about a single parameter at a specified significance level and power.…

聚类数据的半参数回归AI 解读

We consider estimation in a semiparametric partially generalised linear model for clustered data using estimating equations. A marginal model is assumed where the mean of the outcome variable depends on some covariates parametrically and a cluster‐level covariate nonparametrically. A profile‐kernel method allowing for working correlation matrices is developed. We show that the nonparametric part of the model can be estimated using standard nonparametric methods, including…

稳健检验的高阶渐近展开AI 解读

This paper provides high‐order asymptotic expansions for the M‐ratio and the signed‐root M‐ratio robust test statistics, which allow one to compute accurate approximations to significance or critical values using the Edgeworth approximation, the Bartlett correction, the variance correction or the saddlepoint approximation. Specific results are obtained for the linear regression model with the Huber M‐estimator. A Monte Carlo study illustrates the numerical accuracy of these…

基于自由结点样条的贝叶斯曲线拟合AI 解读

We describe a Bayesian method, for fitting curves to data drawn from an exponential family, that uses splines for which the number and locations of knots are free parameters. The method uses reversible‐jump Markov chain Monte Carlo to change the knot configurations and a locality heuristic to speed up mixing. For nonnormal models, we approximate the integrated likelihood ratios needed to compute acceptance probabilities by using the Bayesian information criterion, BIC, under…

基于测度空间变分分析的聚类方法AI 解读

We formulate clustering as a minimisation problem in the space of measures by modelling the cluster centres as a Poisson process with unknown intensity function. We derive a Ward‐type clustering criterion which, under the Poisson assumption, can easily be evaluated explicitly in terms of the intensity function. We show that asymptotically, i.e. for increasing total intensity, the optimal intensity function is proportional to a dimension‐dependent power of the density of the…

用于有序响应变量正关联分析的边际回归模型AI 解读

Given a set of discrete response variables, some of which are ordinal, and an arbitrary set of discrete explanatory variables, we propose a simple matrix formulation for parameterising the saturated model as in Glonek (1996). This is such that, within a hierarchical structure, marginal logits and log‐odds ratios of various possible types, together with the remaining log‐linear interactions of high order, may be modelled by equality and inequality constraints. Inequality…

层级广义线性模型：广义线性、随机效应与结构化离散度的统一AI 解读

Hierarchical generalised linear models are developed as a synthesis of generalised linear models, mixed linear models and structured dispersions. We generalise the restricted maximum likelihood method for the estimation of dispersion to the wider class and show how the joint fitting of models for mean and dispersion can be expressed by two interconnected generalised linear models. The method allows models with (i) any combination of a generalised linear model distribution…

用于最大化条件似然函数的 TM 算法AI 解读

This paper describes an algorithm for maximising a conditional likelihood function when the corresponding unconditional likelihood function is more easily maximised. The algorithm is similar to the EM algorithm but different as the parameters rather than the data are augmented and the conditional rather than the marginal likelihood function is maximised. In exponential families the algorithm takes a particular simple form which is computationally very close to the EM…

周期图平滑窗口选择的简便广义交叉验证方法AI 解读

A consistent estimator for the spectral density of a stationary random process can be obtained by smoothing the periodograms across frequency. An important component of smoothing is the choice of the span. Lee (1997) proposed a span selector that was erroneously claimed to be unbiased for the mean squared error. The naive use of mean squared error has some important drawbacks in this context because the variance of the periodogram depends on its mean, i.e. the spectrum. We…

条件异方差下部分非平稳多元自回归模型的估计AI 解读

This paper investigates a partially nonstationary multivariate autoregressive model, which allows its innovations to be generated by a multivariate ARCH, autoregressive conditional heteroscedastic, process. Three estimators, including the least squares estimator, a full‐rank maximum likelihood estimator and a reduced‐rank maximum likelihood estimator, are considered and their asymptotic distributions are derived. When the multivariate ARCH process reduces to the innovation…

簇内重抽样AI 解读

Within‐cluster resampling is proposed as a new method for analysing clustered data. Although the focus of this paper is clustered binary data, the within‐cluster resampling asymptotic theory is general for many types of clustered data. Within‐cluster resampling is a simple but computationally intensive estimation method. Its main advantage over other marginal analysis methods, such as generalised estimating equations (Liang & Zeger, 1986; Zeger & Liang, 1986) is that it…