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纵向数据边际回归样条的渐近性质AI 解读

There have been studies on how the asymptotic efficiency of a nonparametric function estimator depends on the handling of the within-cluster correlation when nonparametric regression models are used on longitudinal or cluster data. In particular, methods based on smoothing splines and local polynomial kernels exhibit different behaviour. We show that the generalized estimation equations based on weighted least squares regression splines for the nonparametric function have an…

竞争风险及复杂多状态模型的非参数分位数推断札记AI 解读

Nonparametric quantile inference for competing risks has recently been studied by Peng & Fine (2007). Their key result establishes uniform consistency and weak convergence of the inverse of the Aalen–Johansen estimator of the cumulative incidence function, using the representation of the cumulative incidence estimator as a sum of independent and identically distributed random variables. The limit process is of a form similar to that of the standard survival result, but with…

利用随机逼近算法估计错误发现率AI 解读

Testing of multiple hypotheses involves statistics that are strongly dependent in some applications, but most work on this subject is based on the assumption of independence. We propose a new method for estimating the false discovery rate of multiple hypothesis tests, in which the density of test scores is estimated parametrically by minimizing the Kullback–Leibler distance between the unknown density and its estimator using the stochastic approximation algorithm, and the…

删失条件下 Kendall's tau 的一致性AI 解读

Necessary and sufficient conditions for consistency of a simple estimator of Kendall's tau under bivariate censoring are presented. The results are extended to data subject to bivariate left truncation as well as right censoring.

年龄—时期—队列模型与扩展链梯模型的识别AI 解读

We consider the identification problem that arises in the age-period-cohort models as well as in the extended chain-ladder model. We propose a canonical parameterization based on the accelerations of the trends in the three factors. This parameterization is exactly identified and eases interpretation, estimation and forecasting. The canonical parameterization is applied to a class of index sets which have trapezoidal shapes, including various Lexis diagrams and the…

利用主成分联合建模成对稀疏函数数据AI 解读

We propose a modelling framework to study the relationship between two paired longitudinally observed variables. The data for each variable are viewed as smooth curves measured at discrete time-points plus random errors. While the curves for each variable are summarized using a few important principal components, the association of the two longitudinal variables is modelled through the association of the principal component scores. We use penalized splines to model the mean…

线性模型中无限多个对比的 Benjamini–Hochberg 方法AI 解读

Benjamini and Hochberg's method for controlling the false discovery rate is applied to the problem of testing infinitely many contrasts in linear models. Exact, easily calculated critical values are derived, defining a new multiple comparisons method for testing contrasts in linear models. The method is adaptive, depending on the data through the F-statistic, like the Waller–Duncan Bayesian multiple comparisons method. Comparisons with Scheffé's method are given, and the…

响应缺失下基于半参数模型的推断AI 解读

We consider a semiparametric model that parameterizes the conditional density of the response, given covariates, but allows the marginal distribution of the covariates to be completely arbitrary. Responses may be missing. A likelihood-based imputation estimator and a semi-empirical-likelihood-based estimator for the parameter vector describing the conditional density are defined and proved to be asymptotically normal. Semi-empirical loglikelihood functions for the parameter…

影响函数与稳健贝叶斯、经验贝叶斯小区域估计AI 解读

We introduce new robust small area estimation procedures based on area-level models. We first find influence functions corresponding to each individual area-level observation by measuring the divergence between the posterior density functions of regression coefficients with and without that observation. Next, based on these influence functions, properly standardized, we propose some new robust Bayes and empirical Bayes small area estimators. The mean squared errors and…

抽样调查加权与推断的新方法AI 解读

The validity of design-based inference is not dependent on any model assumption. However, it is well known that estimators derived through design-based theory may be inefficient for the estimation of population totals when the design weights are weakly related to the variables of interest and have widely dispersed values. We propose estimators that have the potential to improve the efficiency of any estimator derived under the design-based theory. Our main focus is limited…

线性模型下最优抽样与估计策略AI 解读

In some cases model-based and model-assisted inferences can lead to very different estimators. These two paradigms are not so different if we search for an optimal strategy rather than just an optimal estimator, a strategy being a pair composed of a sampling design and an estimator. We show that, under a linear model, the optimal model-assisted strategy consists of a balanced sampling design with inclusion probabilities that are proportional to the standard deviations of the…

比较两阶段自适应治疗策略的上确界加权对数秩检验与样本量AI 解读

In two-stage adaptive treatment strategies, patients receive an induction treatment followed by a maintenance therapy, given that the patient responded to the induction treatment they received. To test for a difference in the effects of different induction and maintenance treatment combinations, a modified supremum weighted log-rank test is proposed. The test is applied to a dataset from a two-stage randomized trial and the results are compared to those obtained using a…

大模型空间下用于模型选择的扩展贝叶斯信息准则AI 解读

The ordinary Bayesian information criterion is too liberal for model selection when the model space is large. In this paper, we re-examine the Bayesian paradigm for model selection and propose an extended family of Bayesian information criteria, which take into account both the number of unknown parameters and the complexity of the model space. Their consistency is established, in particular allowing the number of covariates to increase to infinity with the sample size.…

利用中位数与球面主成分进行稳健函数估计AI 解读

We present robust estimators for the mean and the principal components of a stochastic process in . Robustness and asymptotic properties of the estimators are studied theoretically, by simulation and by example. It is shown that the proposed estimators are generally more robust to outliers than the commonly used sample mean and principal components, although their properties depend on the spacings of the eigenvalues of the covariance function. Copyright 2008, Oxford…

效应估计中的调整不确定性AI 解读

Often there is substantial uncertainty in the selection of confounders when estimating the association between an exposure and health. We define this type of uncertainty as `adjustment uncertainty'. We propose a general statistical framework for handling adjustment uncertainty in exposure effect estimation for a large number of confounders, we describe a specific implementation, and we develop associated visualization tools. Theoretical results and simulation studies show…

线性混合效应模型条件 AIC 的推广AI 解读

The conventional model selection criterion AIC has been applied to choose candidate models in mixed-effects models by the consideration of marginal likelihood. Vaida and Blanchard (2005) demonstrated that such a marginal AIC and its small sample correction are inappropriate when the research focus is on clusters. Correspondingly, these authors suggested to use conditional AIC. The conditional AIC is derived under the assumptions of the variance-covariance matrix or scaled…

在合理响应模型下用校准加权调整无响应AI 解读

When we estimate the population total for a survey variable or variables, calibration forces the weighted estimates of certain covariates to match known or alternatively estimated population totals called benchmarks. Calibration can be used to correct for sample-survey nonresponse, or for coverage error resulting from frame undercoverage or unit duplication. The quasi-randomization theory supporting its use in nonresponse adjustment treats response as an additional phase of…

含测量误差的加性部分线性模型AI 解读

We consider statistical inference for additive partial linear models when the linear covariate is measured with error. We propose attenuation-to-correction and simulation-extrapolation, simex, estimators of the parameter of interest. It is shown that the first resulting estimator is asymptotically normal and requires no undersmoothing. This is an advantage of our estimator over existing backfitting-based estimators for semiparametric additive models which require…

纵向数据的广义变系数模型AI 解读

We propose a generalization of the varying coefficient model for longitudinal data to cases where not only current but also recent past values of the predictor process affect current response. More precisely, the targeted regression coefficient functions of the proposed model have sliding window supports around current time t. A variant of a recently proposed two-step estimation method for varying coefficient models is proposed for estimation in the context of these…

指数族推断中无条件参数自助法的条件性质AI 解读

Higher-order inference about a scalar parameter in the presence of nuisance parameters can be achieved by bootstrapping, in circumstances where the parameter of interest is a component of the canonical parameter in a full exponential family. The optimal test, which is approximated, is a conditional one based on conditioning on the sufficient statistic for the nuisance parameter. A bootstrap procedure that ignores the conditioning is shown to have desirable conditional…

利用辅助协变量提高对数秩检验的效率AI 解读

Under the assumption of proportional hazards, the log-rank test is optimal for testing the null hypothesis ⁠, where denotes the logarithm of the hazard ratio. However, if there are additional covariates that correlate with survival times, making use of their information will increase the efficiency of the log-rank test. We apply the theory of semiparametrics to characterize a class of regular and asymptotically linear estimators for when auxiliary covariates are incorporated…

加权 Hochberg 多重检验程序AI 解读

We consider different ways of constructing weighted Hochberg-type step-up multiple test procedures including closed procedures based on weighted Simes tests and their conservative step-up short-cuts, and step-up counterparts of two weighted Holm procedures. It is shown that the step-up counterparts have some serious pitfalls such as lack of familywise error rate control and lack of monotonicity in rejection decisions in terms of p-values. Therefore an exact closed procedure…

条件异方差分数单整 ARMA 模型的最小绝对偏差估计AI 解读

We consider a unified least absolute deviation estimator for stationary and nonstationary fractionally integrated autoregressive moving average models with conditional heteroscedasticity. Its asymptotic normality is established when the second moments of errors and innovations are finite. Several other alternative estimators are also discussed and are shown to be less efficient and less robust than the proposed approach. A diagnostic tool, consisting of two portmanteau…

一族贝叶斯多重检验程序AI 解读

Under the model of independent test statistics, we propose a two-parameter family of Bayes multiple testing procedures. The two parameters can be viewed as tuning parameters. Using the Benjamini–Hochberg step-up procedure for controlling false discovery rate as a baseline for conservativeness, we choose the tuning parameters to compromise between the operating characteristics of that procedure and a less conservative procedure that focuses on alternatives that a priori might…