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通过得分贡献符号翻转实现广义线性模型的稳健检验AI 解读

Summary Generalized linear models are often misspecified because of overdispersion, heteroscedasticity and ignored nuisance variables. Existing quasi-likelihood methods for testing in misspecified models often do not provide satisfactory type I error rate control. We provide a novel semiparametric test, based on sign flipping individual score contributions. The parameter tested is allowed to be multi-dimensional and even high dimensional. Our test is often robust against the…

通过自标准化检验函数型时间序列的实质性差异AI 解读

Summary We develop methodology for testing relevant hypotheses about functional time series in a tuning-free way. Instead of testing for exact equality, e.g. for the equality of two mean functions from two independent time series, we propose to test the null hypothesis of no relevant deviation. In the two-sample problem this means that an L2-distance between the two mean functions is smaller than a prespecified threshold. For such hypotheses self-normalization, which was…

两阶段抽样设计的统计推断AI 解读

Summary Two-stage sampling designs are commonly used for household and health surveys. To produce reliable estimators with associated confidence intervals, some basic statistical properties like consistency and asymptotic normality of the Horvitz–Thompson estimator are desirable, along with the consistency of associated variance estimators. These properties have been mainly studied for single-stage sampling designs. In this work, we prove the consistency of the…

利用耦合构造无偏马尔可夫链蒙特卡洛方法AI 解读

Summary Markov chain Monte Carlo (MCMC) methods provide consistent approximations of integrals as the number of iterations goes to ∞. MCMC estimators are generally biased after any fixed number of iterations. We propose to remove this bias by using couplings of Markov chains together with a telescopic sum argument of Glynn and Rhee. The resulting unbiased estimators can be computed independently in parallel. We discuss practical couplings for popular MCMC algorithms. We…

空间数据密度估计的带宽选择AI 解读

Summary Bandwidth choice is crucial in spatial kernel estimation in exploring non-Gaussian complex spatial data. The paper investigates the choice of adaptive and non-adaptive bandwidths for density estimation given data on a spatial lattice. An adaptive bandwidth depends on local data and hence adaptively conforms with local features of the spatial data. We propose a spatial cross-validation (SCV) choice of a global bandwidth. This is done first with a pilot density…

利用稀疏线性规划优化两阶段自适应富集随机试验设计AI 解读

Summary Adaptive enrichment designs involve preplanned rules for modifying enrolment criteria based on accruing data in a randomized trial. We focus on designs where the overall population is partitioned into two predefined subpopulations, e.g. based on a biomarker or risk score measured at baseline. The goal is to learn which populations benefit from an experimental treatment. Two critical components of adaptive enrichment designs are the decision rule for modifying…

通过稳健梯度估计实现稳健估计AI 解读

Summary We provide a new computationally efficient class of estimators for risk minimization. We show that these estimators are robust for general statistical models, under varied robustness settings, including in the classical Huber ε-contamination model, and in heavy-tailed settings. Our workhorse is a novel robust variant of gradient descent, and we provide conditions under which our gradient descent variant provides accurate estimators in a general convex risk…

随机干预的因果中介分析AI 解读

Summary Mediation analysis in causal inference has traditionally focused on binary exposures and deterministic interventions, and a decomposition of the average treatment effect in terms of direct and indirect effects. We present an analogous decomposition of the population intervention effect, defined through stochastic interventions on the exposure. Population intervention effects provide a generalized framework in which a variety of interesting causal contrasts can be…

用于稀疏且具有重叠社区结构图的可交换随机测度AI 解读

Summary We propose a novel statistical model for sparse networks with overlapping community structure. The model is based on representing the graph as an exchangeable point process and naturally generalizes existing probabilistic models with overlapping block structure to the sparse regime. Our construction builds on vectors of completely random measures and has interpretable parameters, each node being assigned a vector representing its levels of affiliation to some latent…

时变随机对象的函数型模型AI 解读

Summary Functional data analysis provides a popular toolbox of functional models for the analysis of samples of random functions that are real valued. In recent years, samples of time-varying object data such as time-varying networks that are not in a vector space have been increasingly collected. These data can be viewed as elements of a general metric space that lacks local or global linear structure and therefore common approaches that have been used with great success…

右奇异向量投影图：潜在混杂下的快速高维协方差估计AI 解读

Summary We consider the problem of estimating a high dimensional p × p covariance matrix Σ, given n observations of confounded data with covariance Σ+ΓΓT, where Γ is an unknown p × q matrix of latent factor loadings. We propose a simple and scalable estimator based on the projection onto the right singular vectors of the observed data matrix, which we call right singular vector projection (RSVP). Our theoretical analysis of this method reveals that, in contrast with…

基于轴对齐随机投影的稀疏主成分分析AI 解读

Summary We introduce a new method for sparse principal component analysis, based on the aggregation of eigenvector information from carefully selected axis-aligned random projections of the sample covariance matrix. Unlike most alternative approaches, our algorithm is non-iterative, so it is not vulnerable to a bad choice of initialization. We provide theoretical guarantees under which our principal subspace estimator can attain the minimax optimal rate of convergence in…

Sumca：蒙特卡洛辅助的二阶无偏均方预测误差估计AI 解读

Summary We propose a simple, unified, Monte-Carlo-assisted approach (called ‘Sumca’) to second-order unbiased estimation of the mean-squared prediction error (MSPE) of a small area predictor. The MSPE estimator proposed is easy to derive, has a simple expression and applies to a broad range of predictors that include the traditional empirical best linear unbiased predictor, empirical best predictor and post-model-selection empirical best linear unbiased predictor and…

分类未观测混杂下双重负控调整的多重稳健因果推断AI 解读

Summary Unmeasured confounding is a threat to causal inference in observational studies. In recent years, the use of negative controls to mitigate unmeasured confounding has gained increasing recognition and popularity. Negative controls have a long-standing tradition in laboratory sciences and epidemiology to rule out non-causal explanations, although they have been used primarily for bias detection. Recently, Miao and colleagues have described sufficient conditions under…

高维线性回归解释方差的半监督推断及其应用AI 解读

Summary The paper considers statistical inference for the explained variance βTΣβ under the high dimensional linear model Y = Xβ + ε in the semisupervised setting, where β is the regression vector and Σ is the design covariance matrix. A calibrated estimator, which efficiently integrates both labelled and unlabelled data, is proposed. It is shown that the estimator achieves the minimax optimal rate of convergence in the general semisupervised framework. The optimality result…

近似贝叶斯计算中的模型误设：后果与诊断AI 解读

Summary We analyse the behaviour of approximate Bayesian computation (ABC) when the model generating the simulated data differs from the actual data-generating process, i.e. when the data simulator in ABC is misspecified. We demonstrate both theoretically and in simple, but practically relevant, examples that when the model is misspecified different versions of ABC can yield substantially different results. Our theoretical results demonstrate that even though the model is…

高维数据下合并概率与非概率样本的双重稳健推断AI 解读

Summary We consider integrating a non-probability sample with a probability sample which provides high dimensional representative covariate information of the target population. We propose a two-step approach for variable selection and finite population inference. In the first step, we use penalized estimating equations with folded concave penalties to select important variables and show selection consistency for general samples. In the second step, we focus on a doubly…

利用个性化PageRank对巨型分块模型图进行定向抽样AI 解读

Summary The paper provides statistical theory and intuition for personalized PageRank (called ‘PPR’): a popular technique that samples a small community from a massive network. We study a setting where the entire network is expensive to obtain thoroughly or to maintain, but we can start from a seed node of interest and ‘crawl’ the network to find other nodes through their connections. By crawling the graph in a designed way, the PPR vector can be approximated without…

再随机化与回归调整AI 解读

Summary Randomization is a basis for the statistical inference of treatment effects without strong assumptions on the outcome-generating process. Appropriately using covariates further yields more precise estimators in randomized experiments. R. A. Fisher suggested blocking on discrete covariates in the design stage or conducting analysis of covariance in the analysis stage. We can embed blocking in a wider class of experimental design called rerandomization, and extend the…

流式数据广义线性模型的可更新估计与增量推断AI 解读

Summary The paper presents an incremental updating algorithm to analyse streaming data sets using generalized linear models. The method proposed is formulated within a new framework of renewable estimation and incremental inference, in which the maximum likelihood estimator is renewed with current data and summary statistics of historical data. Our framework can be implemented within a popular distributed computing environment, known as Apache Spark, to scale up computation.…

基于随机偏微分方程的多元 G 型 Matérn 随机场AI 解读

Summary For many applications with multivariate data, random-field models capturing departures from Gaussianity within realizations are appropriate. For this reason, we formulate a new class of multivariate non-Gaussian models based on systems of stochastic partial differential equations with additive type G noise whose marginal covariance functions are of Matérn type. We consider four increasingly flexible constructions of the noise, where the first two are similar to…

理解敏感性：扩展遗漏变量偏误分析AI 解读

Summary We extend the omitted variable bias framework with a suite of tools for sensitivity analysis in regression models that does not require assumptions on the functional form of the treatment assignment mechanism nor on the distribution of the unobserved confounders, naturally handles multiple confounders, possibly acting non-linearly, exploits expert knowledge to bound sensitivity parameters and can be easily computed by using only standard regression results. In…

时间序列误差下非参数回归的多尺度推断与长期方差估计AI 解读

Summary We develop new multiscale methods to test qualitative hypotheses about the function m in the non-parametric regression model Yt, T = m(t/T) + ɛt with time series errors ɛt. In time series applications, m represents a non-parametric time trend. Practitioners are often interested in whether the trend m has certain shape properties. For example, they would like to know whether m is constant or whether it is increasing or decreasing in certain time intervals. Our…

基于Pólya树的相关密度贝叶斯层级模型AI 解读

Summary Bayesian hierarchical models are used to share information between related samples and to obtain more accurate estimates of sample level parameters, common structure and variation between samples. When the parameter of interest is the distribution or density of a continuous variable, a hierarchical model for continuous distributions is required. Various such models have been described in the literature using extensions of the Dirichlet process and related processes,…