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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…

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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…

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…

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…

渐消加权区块自助法AI 解读

We introduce and study tapered block bootstrap methodology that yields an improvement over the well‐known block bootstrap for time series of Künsch (1989). The asymptotic validity and the favourable bias properties of the tapered block bootstrap are shown. The important practical issues of optimally choosing the window shape and the block size are addressed in detail, while some finite‐sample simulations are presented validating the good performance of the tapered block…

长程相依的贝叶斯半参数推断AI 解读

We develop a Bayesian semiparametric procedure for the analysis of stationary long‐range dependent time series. We use frequency domain methods to partition the infinite‐dimensional parameter space into regions where genuine prior information on the form of the spectral density is available, and others where vague prior beliefs are adopted; the solution to the partition problem, which is equivalent to bandwidth choice from a frequentist point of view, is obtained via Bayes…

We extend Robins’ theory of causal inference for complex longitudinal data to the case of continuously varying as opposed to discrete covariates and treatments. In particular we establish versions of the key results of the discrete theory: the $g$-computation formula and a collection of powerful characterizations of the $g$-null hypothesis of no treatment effect. This is accomplished under natural continuity hypotheses concerning the conditional distributions of the outcome…

单调函数的似然比检验AI 解读

We study the problem of testing for equality at a fixed point in the setting of nonparametric estimation of a monotone function.The likelihood ratio test for this hypothesis is derived in the particular case of interval censoring (or current status data)and its limiting distribution is obtained. The limiting distribution is that of the integral of the difference of the squared slope processes corresponding to a canonical version of the problem involving Brownian motion $+t^2$…

凸函数估计：估计量刻画与渐近理论AI 解读

We study nonparametric estimation of convexregression and density functions by methods of least squares (in the regression and density cases) and maximum likelihood (in the density estimation case).We provide characterizations of these estimators, prove that they are consistent and establish their asymptotic distributions at a fixed point of positive curvature of the functions estimated. The asymptotic distribution theory relies on the existence of an “invelope function” for…

求职搜寻模型中的最优性检验AI 解读

Models of search in labor markets are potentially of great use for policy analy-sis since their parameters are structural. However, a common feature of these models is that an assumption of optimal behavior on the part of agents is necessary to achieve identifica-tion. From a classical econometric perspective, this means the assumption of optimality is untestable and, if optimality is not imposed, it is impossible to learn about the unidentified parameters. This paper argues…

The properties of a range of maximum eigenvalue and trace tests for the cointegrating rank of a vector autoregressive process are compared. The tests are all likelihood ratio-type tests and operate under different assumptions regarding the deterministic part of the data generation process. The asymptotic distributions under local alternatives are given and the local power is derived. It is found that the local power of corresponding maximum eigenvalue and trace tests is very…

AR(1) 单位根检验 t 比率的极限分布AI 解读

We consider the limiting distribution of the t -statistic for testing the random walk hypothesis in the classical Gaussian AR(1) model. Abadir (1995, Econometric Theory, 11, 775�793) derived the first derives a closed (i.e. integration-free) expression for the limit-ing distribution function. This paper derives an alternative closed expression. Abadir�s and the new expression are valid only for negative arguments and each involve two infinite summa-tions. To enable a…

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无需向量自回归的简易协整秩检验AI 解读

This paper proposes a fully nonparametric test for cointegrating rank which does not require estimation of a vector autoregressive model. The test exploits the fact that the degeneracy in the moment matrix of the variables with mixed integration order corresponds to the notion of cointegration. With an appropriate standardization, the test statistics are shown to have a nuisance parameter free limiting distribution and to be consistent under reasonable conditions. Monte…