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最小化及其他协变量自适应随机化下的平均处理效应推断AI 解读

Summary Covariate-adaptive randomization schemes such as minimization and stratified permuted blocks are often applied in clinical trials to balance treatment assignments across prognostic factors. The existing theory for inference after covariate-adaptive randomization is mostly limited to situations where a correct model between the response and covariates can be specified or the randomization method has well-understood properties. Based on stratification with covariate…

稀疏信号的最优选择后推断：非参数经验贝叶斯方法AI 解读

Summary Many recently developed Bayesian methods focus on sparse signal detection. However, much less work has been done on the natural follow-up question: how does one make valid inferences for the magnitude of those signals after selection? Ordinary Bayesian credible intervals suffer from selection bias, as do ordinary frequentist confidence intervals. Existing Bayesian methods for correcting this bias produce credible intervals with poor frequentist properties. Further,…

考虑异质性且通信高效的分布式统计推断AI 解读

Summary In multicentre research, individual-level data are often protected against sharing across sites. To overcome the barrier of data sharing, many distributed algorithms, which only require sharing aggregated information, have been developed. The existing distributed algorithms usually assume the data are homogeneously distributed across sites. This assumption ignores the important fact that the data collected at different sites may come from various subpopulations and…

用于独立性检验的点间排序符号协方差AI 解读

Summary We generalize the sign covariance introduced by Bergsma & Dassios (2014) to multivariate random variables and beyond. The new interpoint-ranking sign covariance is applicable to general types of random objects as long as a meaningful similarity measure can be defined, and it is shown to be zero if and only if the two random variables are independent. The test statistic is a $U$-statistic, whose large-sample behaviour guarantees that the proposed test is consistent…

改进错误覆盖率调整的选择性置信区间的一般方法AI 解读

Summary Post-selection inference on thousands of parameters has attracted considerable research interest in recent years. Specifically, Benjamini & Yekutieli (2005) considered constructing confidence intervals after selection. They proposed adjusting the confidence levels of marginal confidence intervals for the selected parameters to ensure control of the false coverage-statement rate. However, although Benjamini–Yekutieli confidence intervals are widely used, they are…

协变量维数发散时的积分条件矩检验及其扩展AI 解读

Summary The classical integrated conditional moment test is a promising method for model checking and its basic idea has been applied to develop several variants. However, in diverging-dimension scenarios, the integrated conditional moment test may break down and has completely different limiting properties from the fixed-dimension case. Furthermore, the related wild bootstrap approximation can also be invalid. To extend this classical test to diverging dimension settings,…

计数过程形状与规模指标的统计推断AI 解读

Summary Single-index models have gained increased popularity in time-to-event analysis owing to their model flexibility and advantage in dimension reduction. We propose a semiparametric framework for the rate function of a recurrent event counting process by modelling its size and shape components with single-index models. With additional monotone constraints on the two link functions for the size and shape components, the proposed model possesses the desired directional…

序贯蒙特卡洛的分层与最优重采样AI 解读

Summary Sequential Monte Carlo algorithms are widely accepted as powerful computational tools for making inference with dynamical systems. A key step in sequential Monte Carlo is resampling, which plays the role of steering the algorithm towards the future dynamics. Several strategies have been used in practice, including multinomial resampling, residual resampling, optimal resampling, stratified resampling and optimal transport resampling. In one-dimensional cases, we show…

误设广义线性模型中的大规模模型选择AI 解读

Summary Model selection is crucial both to high-dimensional learning and to inference for contemporary big data applications in pinpointing the best set of covariates among a sequence of candidate interpretable models. Most existing work implicitly assumes that the models are correctly specified or have fixed dimensionality, yet both model misspecification and high dimensionality are prevalent in practice. In this paper, we exploit the framework of model selection principles…

极值指数的分布式推断AI 解读

Summary In this paper we investigate a divide-and-conquer algorithm for estimating the extreme value index when data are stored in multiple machines. The oracle property of such an algorithm based on extreme value methods is not guaranteed by the general theory of distributed inference. We propose a distributed Hill estimator and establish its asymptotic theories. We consider various cases where the number of observations involved in each machine can be either homogeneous or…

广义结构模型中的回代检验AI 解读

Summary We introduce bootstrap tests for semiparametric generalized structured models. These can be used for testing different kinds of model specifications like separability, functional forms and homogeneity of effects, or for performing variable selection in a large class of semiparametric models. The test statistics are based on the comparison of non- and semiparametric alternatives in which both the null hypothesis and the alternative are non- or semiparametric. All…

高斯差分隐私AI 解读

Abstract In the past decade, differential privacy has seen remarkable success as a rigorous and practical formalization of data privacy. This privacy definition and its divergence based relaxations, however, have several acknowledged weaknesses, either in handling composition of private algorithms or in analysing important primitives like privacy amplification by subsampling. Inspired by the hypothesis testing formulation of privacy, this paper proposes a new relaxation of…

高维多尺度在线变点检测AI 解读

Abstract We introduce a new method for high-dimensional, online changepoint detection in settings where a p-variate Gaussian data stream may undergo a change in mean. The procedure works by performing likelihood ratio tests against simple alternatives of different scales in each coordinate, and then aggregating test statistics across scales and coordinates. The algorithm is online in the sense that both its storage requirements and worst-case computational complexity per new…

一般干扰下因果效应随机化检验的图论方法AI 解读

Abstract Interference exists when a unit's outcome depends on another unit's treatment assignment. For example, intensive policing on one street could have a spillover effect on neighbouring streets. Classical randomization tests typically break down in this setting because many null hypotheses of interest are no longer sharp under interference. A promising alternative is to instead construct a conditional randomization test on a subset of units and assignments for which a…

高维线性回归的迁移学习：预测、估计与极小极大最优性AI 解读

Abstract This paper considers estimation and prediction of a high-dimensional linear regression in the setting of transfer learning where, in addition to observations from the target model, auxiliary samples from different but possibly related regression models are available. When the set of informative auxiliary studies is known, an estimator and a predictor are proposed and their optimality is established. The optimal rates of convergence for prediction and estimation are…

无浪费序贯蒙特卡洛AI 解读

Abstract A standard way to move particles in a sequential Monte Carlo (SMC) sampler is to apply several steps of a Markov chain Monte Carlo (MCMC) kernel. Unfortunately, it is not clear how many steps need to be performed for optimal performance. In addition, the output of the intermediate steps are discarded and thus wasted somehow. We propose a new, waste-free SMC algorithm which uses the outputs of all these intermediate MCMC steps as particles. We establish that its…

推断型 Wasserstein 生成对抗网络AI 解读

Abstract Generative adversarial networks (GANs) have been impactful on many problems and applications but suffer from unstable training. The Wasserstein GAN (WGAN) leverages the Wasserstein distance to avoid the caveats in the minmax two-player training of GANs but has other defects such as mode collapse and lack of metric to detect the convergence. We introduce a novel inferential Wasserstein GAN (iWGAN) model, which is a principled framework to fuse autoencoders and WGANs.…

广义线性混合模型分析与设计的可用精确渐近结果AI 解读

Abstract We derive precise asymptotic results that are directly usable for confidence intervals and Wald hypothesis tests for likelihood-based generalized linear mixed model analysis. The essence of our approach is to derive the exact leading term behaviour of the Fisher information matrix when both the number of groups and number of observations within each group diverge. This leads to asymptotic normality results with simple studentizable forms. Similar analyses result in…

促进时间治愈模型的一种扩展AI 解读

We consider the problem of estimating the distribution of time-to-event data that is subject to censoring and for which the event of interest might never occur, that is, some subjects are cured. To model this kind of data in the presence of covariates, one of the leading semiparametric models is the promotion time cure model (Stochastic Models of Tumor Latency and Their Biostatistical Applications (1996) World Scientific), which adapts the Cox model to the presence of cured…

多变量纵向与生存数据的半参数潜在类别模型AI 解读

In long-term follow-up studies, data are often collected on repeated measures of multivariate response variables as well as on time to the occurrence of a certain event. To jointly analyze such longitudinal data and survival time, we propose a general class of semiparametric latent-class models that accommodates a heterogeneous study population with flexible dependence structures between the longitudinal and survival outcomes. We combine nonparametric maximum likelihood…

纯量子态的极小极大非参数估计AI 解读

In classical statistics, Pinsker’s theorem provides an exact asymptotic minimax bound in nonparametric estimation, improving upon optimal rates of convergence results. We obtain a quantum version of the theorem by establishing asymptotic minimax results for estimation of the displacement vector in a quantum Gaussian white noise model, given by a sequence of shifted vacuum states. Analogous results are then obtained for estimation of a general pure state from an ensemble of…

凸约束高斯序列模型中似然比检验的高维渐近理论AI 解读

In the Gaussian sequence model Y=μ+ξ, we study the likelihood ratio test (LRT) for testing H0:μ=μ0 versus H1:μ∈K, where μ0∈K, and K is a closed convex set in Rn. In particular, we show that under the null hypothesis, normal approximation holds for the log-likelihood ratio statistic for a general pair (μ0,K), in the high-dimensional regime where the estimation error of the associated least squares estimator diverges in an appropriate sense. The normal approximation further…

任意依赖下合并p值的可容许方法AI 解读

Methods of merging several p-values into a single p-value are important in their own right and widely used in multiple hypothesis testing. This paper is the first to systematically study the admissibility (in Wald’s sense) of p-merging functions and their domination structure, without any information on the dependence structure of the input p-values. As a technical tool, we use the notion of e-values, which are alternatives to p-values recently promoted by several authors.…

置换检验的极小极大最优性AI 解读

Permutation tests are widely used in statistics, providing a finite-sample guarantee on the type I error rate whenever the distribution of the samples under the null hypothesis is invariant to some rearrangement. Despite its increasing popularity and empirical success, theoretical properties of the permutation test, especially its power, have not been fully explored beyond simple cases. In this paper, we attempt to partly fill this gap by presenting a general nonasymptotic…