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《使用 R 的半参数回归》AI 解读

Semiparametric Regression with R by Harezlak, Ruppert, and Wand is a truly heroic book! To many of us, statistics can be roughly dichotomized into parametric and nonparametric. Semiparametric stati...

贝叶斯稀疏线性回归的神经元化先验AI 解读

Although Bayesian variable selection methods have been intensively studied, their routine use in practice has not caught up with their non-Bayesian counterparts such as Lasso, likely due to difficulties in both computations and flexibilities of prior choices. To ease these challenges, we propose the neuronized priors to unify and extend some popular shrinkage priors, such as Laplace, Cauchy, horseshoe, and spike-and-slab priors. A neuronized prior can be written as the…

时变随机对象与动态网络的建模AI 解读

Samples of dynamic or time-varying networks and other random object data such as time-varying probability distributions are increasingly encountered in modern data analysis. Common methods for time-varying data such as functional data analysis are infeasible when observations are time courses of networks or other complex non-Euclidean random objects that are elements of general metric spaces. In such spaces, only pairwise distances between the data objects are available and…

高维时间序列的断点推断AI 解读

For multiple change-points detection of high-dimensional time series, we provide asymptotic theory concerning the consistency and the asymptotic distribution of the breakpoint statistics and estimated break sizes. The theory backs up a simple two-step procedure for detecting and estimating multiple change-points. The proposed two-step procedure involves the maximum of a MOSUM (moving sum) type statistics in the first step and a CUSUM (cumulative sum) refinement step on an…

有偏抽样下的独立性检验AI 解读

Testing for dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that can create spurious dependence. An important example is truncation models, in which observed pairs are restricted to a specific subset of the X-Y plane. Standard tests for independence are not suitable in such cases, and alternative tests that take the selection bias into account are required. Here, we generalize the…

分位数回归中的单指标门限模型AI 解读

Threshold regression models are useful for identifying subgroups with heterogeneous parameters. The conventional threshold regression models split the sample based on a single and observed threshold variable, which enforces the threshold point to be equal for all subgroups of the population. In this article, we consider a more flexible single-index threshold model in the quantile regression setup, in which the sample is split based on a linear combination of predictors. We…

保护个体数据的高维异质研究整合回归AI 解读

Evidence-based decision making often relies on meta-analyzing multiple studies, which enables more precise estimation and investigation of generalizability. Integrative analysis of multiple heterogeneous studies is, however, highly challenging in the ultra high-dimensional setting. The challenge is even more pronounced when the individual-level data cannot be shared across studies, known as DataSHIELD contraint. Under sparse regression models that are assumed to be similar…

半监督线性回归AI 解读

We study a regression problem where for some part of the data we observe both the label variable (Y) and the predictors (X), while for other part of the data only the predictors are given. Such a problem arises, for example, when observations of the label variable are costly and may require a skilled human agent. When the conditional expectation E[Y|X] is not exactly linear, one can consider the best linear approximation to the conditional expectation, which can be estimated…

聚类分区随机试验的设计型比率估计与中心极限定理AI 解读

This article develops design-based ratio estimators for clustered, blocked randomized controlled trials (RCTs), with an application to a federally funded, school-based RCT testing the effects of behavioral health interventions. We consider finite population weighted least-square estimators for average treatment effects (ATEs), allowing for general weighting schemes and covariates. We consider models with block-by-treatment status interactions as well as restricted models…

数据集偏移下的广义贝叶斯类别比例学习AI 解读

Quantification learning is the task of prevalence estimation for a test population using predictions from a classifier trained on a different population. Quantification methods assume that the sensitivities and specificities of the classifier are either perfect or transportable from the training to the test population. These assumptions are inappropriate in the presence of dataset shift, when the misclassification rates in the training population are not representative of…

多参数非参数融合学习：结合数据深度与置信分布AI 解读

Fusion learning refers to synthesizing inferences from multiple sources or studies to make a more effective inference and prediction than from any individual source or study alone. Most existing methods for synthesizing inferences rely on parametric model assumptions, such as normality, which often do not hold in practice. We propose a general nonparametric fusion learning framework for synthesizing inferences for multiparameters from different studies. The main tool…

网络函数型变系数模型AI 解读

We consider functional responses with network dependence observed for each individual at irregular time points. To model both the interindividual dependence and within-individual dynamic correlation, we propose a network functional varying coefficient (NFVC) model. The response of each individual is characterized by a linear combination of responses from its connected nodes and its exogenous covariates. All the model coefficients are allowed to be time dependent. The NFVC…

高维数据变点的自适应推断AI 解读

In this article, we propose a class of test statistics for a change point in the mean of high-dimensional independent data. Our test integrates the U-statistic based approach in a recent work by Wang et al. and the Lq-norm based high-dimensional test in a recent work by He et al., and inherits several appealing features such as being tuning parameter free and asymptotic independence for test statistics corresponding to even q’s. A simple combination of test statistics…

核常微分方程AI 解读

Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations. We do not assume the functional forms in ODE to be known, or restrict them to be linear or additive, and we allow pairwise interactions. We perform sparse estimation to select individual functionals, and construct confidence intervals for…

结合目标总体汇总统计与源总体个体数据的事件发生风险外推AI 解读

Predicting risks of chronic diseases has become increasingly important in clinical practice. When a prediction model is developed in a cohort, there is a great interest to apply the model to other cohorts. Due to potential discrepancy in baseline disease incidences between different cohorts and shifts in patient composition, the risk predicted by the model built in the source cohort often under- or over-estimates the risk in a new cohort. In this article, we assume the…

时间序列模型的稳健两步小波推断AI 解读

) models with additional stochastic processes are increasingly used for data analysis in biology, ecology, engineering, and economics. Inference on and/or prediction from these models can be highly challenging: (i) the data may contain outliers that can adversely affect the estimation procedure; (ii) the computational complexity can become prohibitive when the time series are extremely large; (iii) model selection adds another layer of (computational) complexity; and (iv)…

嵌套误差回归模型中经验最佳线性无偏预测的渐近理论AI 解读

In this article we derive the asymptotic distribution of estimated best linear unbiased predictors (EBLUPs) of the random effects in a nested error regression model. Under very mild conditions which do not require the assumption of normality, we show that asymptotically the distribution of the EBLUPs as both the number of clusters and the cluster sizes diverge to infinity is the convolution of the true distribution of the random effects and a normal distribution. This result…

预先多重检验估计及其在多样本协方差估计中的应用AI 解读

Multisample covariance estimation—that is, estimation of the covariance matrices associated with k distinct populations—is a classical problem in multivariate statistics. A common solution is to base estimation on the outcome of a test that these covariance matrices show some given pattern. Such a preliminary test may, for example, investigate whether or not the various covariance matrices are equal to each other (test of homogeneity), or whether or not they have common…

利用布尔矩阵逻辑检验中介效应AI 解读

A central question in high-dimensional mediation analysis is to infer the significance of individual mediators. The main challenge is that the total number of potential paths that go through any mediator is super-exponential in the number of mediators. Most existing mediation inference solutions either explicitly impose that the mediators are conditionally independent given the exposure, or ignore any potential directed paths among the mediators. In this article, we propose…

一致稀疏深度学习：理论与计算AI 解读

Deep learning has been the engine powering many successes of data science. However, the deep neural network (DNN), as the basic model of deep learning, is often excessively over-parameterized, causing many difficulties in training, prediction and interpretation. We propose a frequentist-like method for learning sparse DNNs and justify its consistency under the Bayesian framework: the proposed method could learn a sparse DNN with at most O(n/ log (n)) connections and nice…

无需估计非可忽略缺失机制的通用估计程序AI 解读

We consider the estimation problem in a regression setting where the outcome variable is subject to nonignorable missingness and identifiability is ensured by the shadow variable approach. We propose a versatile estimation procedure where modeling of missingness mechanism is completely bypassed. We show that our estimator is easy to implement and we derive the asymptotic theory of the proposed estimator. We also investigate some alternative estimators under different…

普通最小二乘二次泛函的中等维度推断AI 解读

Statistical inferences for quadratic functionals of linear regression parameter have found wide applications including signal detection, global testing, inferences of error variance and fraction of variance explained. Classical theory based on ordinary least squares estimator works perfectly in the low-dimensional regime, but fails when the parameter dimension pn grows proportionally to the sample size n. In some cases, its performance is not satisfactory even when n≥5pn.…

高维线性混合效应模型的推断：拟似然方法AI 解读

Linear mixed-effects models are widely used in analyzing clustered or repeated measures data. We propose a quasi-likelihood approach for estimation and inference of the unknown parameters in linear mixed-effects models with high-dimensional fixed effects. The proposed method is applicable to general settings where the dimension of the random effects and the cluster sizes are possibly large. Regarding the fixed effects, we provide rate optimal estimators and valid inference…

用于分布式估计与推断的一阶牛顿型估计量AI 解读

This article studies distributed estimation and inference for a general statistical problem with a convex loss that could be nondifferentiable. For the purpose of efficient computation, we restrict ourselves to stochastic first-order optimization, which enjoys low per-iteration complexity. To motivate the proposed method, we first investigate the theoretical properties of a straightforward divide-and-conquer stochastic gradient descent approach. Our theory shows that there…